From 080382f0e4d5c2637d4099177e04a8086c1542ee Mon Sep 17 00:00:00 2001 From: astamm Date: Wed, 11 Dec 2024 16:52:06 +0000 Subject: [PATCH] =?UTF-8?q?Deploying=20to=20gh-pages=20from=20@=20astamm/n?= =?UTF-8?q?evada@fedec9749092193c32444e84a6e79676d7b576c8=20=F0=9F=9A=80?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- articles/nevada.html | 292 +++++++++++++++++++++---------------------- index.html | 2 +- pkgdown.yml | 2 +- search.json | 2 +- sitemap.xml | 1 - 5 files changed, 149 insertions(+), 150 deletions(-) diff --git a/articles/nevada.html b/articles/nevada.html index 62c97e7..bb1b9cf 100644 --- a/articles/nevada.html +++ b/articles/nevada.html @@ -145,163 +145,163 @@ repr_nvd(x, representation = "laplacian") #> [[1]] #> [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12] [,13] -#> [1,] 7 -1 0 -1 -1 0 0 0 -1 0 0 0 0 -#> [2,] 0 5 0 -1 0 0 0 0 0 -1 -1 0 -1 -#> [3,] 0 -1 8 0 0 0 -1 0 -1 -1 0 0 -1 -#> [4,] 0 0 0 2 -1 0 0 0 0 0 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+#> [17,] 0 -1 -1 11 0 -1 -1 -1 0 -1 0 +#> [18,] 0 0 0 0 6 0 0 0 0 -1 0 +#> [19,] -1 0 0 0 -1 4 0 0 0 -1 0 +#> [20,] -1 0 -1 0 0 0 9 0 0 -1 -1 +#> [21,] 0 0 0 -1 0 0 0 4 0 -1 0 +#> [22,] -1 0 0 0 -1 -1 -1 0 9 -1 0 +#> [23,] 0 0 0 -1 0 -1 0 -1 0 10 -1 +#> [24,] 0 -1 0 -1 0 0 0 -1 0 0 7 #> attr(,"representation") #> [1] "laplacian" #> #> [[3]] #> [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12] [,13] -#> [1,] 8 -1 0 0 -1 0 0 0 -1 0 0 0 -1 -#> [2,] 0 9 -1 -1 0 -1 0 0 -1 -1 -1 -1 0 -#> [3,] 0 0 4 0 0 0 0 0 -1 0 0 0 -1 -#> [4,] 0 -1 -1 9 0 0 -1 0 -1 0 0 0 -1 -#> [5,] -1 0 0 -1 10 -1 0 -1 -1 -1 0 -1 0 -#> [6,] 0 0 0 -1 -1 9 0 -1 0 0 0 0 -1 -#> [7,] 0 0 0 0 -1 -1 7 0 0 -1 -1 0 0 -#> [8,] -1 0 -1 0 -1 -1 0 11 -1 0 -1 0 -1 -#> [9,] 0 0 0 0 0 0 0 0 4 0 -1 -1 0 -#> [10,] 0 -1 0 0 0 0 0 0 -1 6 0 0 0 -#> [11,] 0 0 0 -1 0 -1 -1 0 -1 -1 10 0 0 -#> [12,] -1 0 -1 -1 -1 -1 0 0 -1 0 0 9 -1 -#> [13,] 0 0 -1 -1 -1 -1 0 0 -1 0 -1 -1 13 -#> [14,] -1 -1 -1 0 0 0 0 0 0 0 0 0 -1 -#> [15,] -1 0 0 0 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-1 0 0 0 0 -#> [18,] 0 -1 0 -1 12 -1 -1 0 0 0 0 -#> [19,] 0 -1 0 -1 -1 9 -1 0 -1 0 0 -#> [20,] 0 -1 0 0 0 0 8 0 0 -1 0 -#> [21,] 0 -1 0 -1 -1 0 -1 11 -1 0 0 -#> [22,] -1 -1 -1 0 -1 0 -1 -1 9 0 0 -#> [23,] 0 0 0 -1 0 -1 -1 0 0 11 -1 -#> [24,] 0 -1 0 -1 0 0 0 0 0 0 5 +#> [1,] 0 0 -1 -1 0 0 0 0 0 0 -1 +#> [2,] 0 0 0 0 0 0 0 0 -1 0 0 +#> [3,] -1 0 0 -1 0 -1 0 0 0 -1 0 +#> [4,] -1 -1 -1 -1 -1 -1 0 0 0 0 0 +#> [5,] 0 0 0 -1 0 0 0 -1 0 0 -1 +#> [6,] 0 0 0 -1 0 -1 -1 0 0 -1 0 +#> [7,] 0 0 0 0 0 0 0 -1 0 0 -1 +#> [8,] -1 0 -1 0 0 0 -1 0 -1 -1 0 +#> [9,] 0 0 -1 0 0 0 -1 -1 0 0 -1 +#> [10,] 0 0 0 -1 -1 0 0 0 -1 -1 0 +#> [11,] -1 0 0 -1 0 0 -1 -1 0 -1 0 +#> [12,] -1 0 0 -1 -1 0 -1 0 -1 0 -1 +#> [13,] 0 0 -1 0 -1 0 0 0 0 -1 0 +#> [14,] 7 0 -1 0 -1 0 0 0 -1 -1 0 +#> [15,] 0 10 0 0 0 -1 -1 0 -1 -1 -1 +#> [16,] -1 0 10 0 -1 0 0 0 -1 -1 0 +#> [17,] 0 0 0 5 0 0 -1 -1 0 -1 -1 +#> [18,] -1 0 0 -1 4 0 0 0 0 0 0 +#> [19,] 0 0 0 0 0 7 -1 0 0 0 0 +#> [20,] -1 0 0 -1 0 0 9 -1 -1 0 0 +#> [21,] -1 -1 0 0 -1 0 -1 11 -1 0 -1 +#> [22,] 0 0 0 0 0 0 -1 0 7 0 0 +#> [23,] -1 0 0 -1 0 -1 0 0 0 8 0 +#> [24,] 0 -1 0 0 0 0 0 0 -1 -1 5 #> attr(,"representation") #> [1] "laplacian" @@ -339,8 +339,8 @@ #> • loops: FALSE dist_nvd(x, representation = "laplacian", distance = "hamming") #> 1 2 -#> 2 0.5760870 -#> 3 0.5271739 0.5307971 +#> 2 0.5869565 +#> 3 0.5996377 0.5416667

Test statistics

diff --git a/index.html b/index.html index 648e711..e53cf0a 100644 --- a/index.html +++ b/index.html @@ -66,7 +66,7 @@

InstallationGitHub with:

 # install.packages("remotes")
-remotes::install_github("astamm/nevada")
+remotes::install_github("astamm/nevada")

Usage diff --git a/pkgdown.yml b/pkgdown.yml index 3caf3cf..fee38f8 100644 --- a/pkgdown.yml +++ b/pkgdown.yml @@ -3,7 +3,7 @@ pkgdown: 2.1.1 pkgdown_sha: ~ articles: nevada: nevada.html -last_built: 2024-12-11T15:58Z +last_built: 2024-12-11T16:51Z urls: reference: https://astamm.github.io/nevada/reference article: https://astamm.github.io/nevada/articles diff --git a/search.json b/search.json index 7d234c6..95d9960 100644 --- a/search.json +++ b/search.json @@ -1 +1 @@ -[{"path":"https://astamm.github.io/nevada/LICENSE.html","id":null,"dir":"","previous_headings":"","what":"GNU General Public License","title":"GNU General Public License","text":"Version 3, 29 June 2007Copyright © 2007 Free Software Foundation, Inc.  Everyone permitted copy distribute verbatim copies license document, changing allowed.","code":""},{"path":"https://astamm.github.io/nevada/LICENSE.html","id":"preamble","dir":"","previous_headings":"","what":"Preamble","title":"GNU General Public License","text":"GNU General Public License free, copyleft license software kinds works. licenses software practical works designed take away freedom share change works. contrast, GNU General Public License intended guarantee freedom share change versions program–make sure remains free software users. , Free Software Foundation, use GNU General Public License software; applies also work released way authors. can apply programs, . speak free software, referring freedom, price. General Public Licenses designed make sure freedom distribute copies free software (charge wish), receive source code can get want , can change software use pieces new free programs, know can things. protect rights, need prevent others denying rights asking surrender rights. Therefore, certain responsibilities distribute copies software, modify : responsibilities respect freedom others. example, distribute copies program, whether gratis fee, must pass recipients freedoms received. must make sure , , receive can get source code. must show terms know rights. Developers use GNU GPL protect rights two steps: (1) assert copyright software, (2) offer License giving legal permission copy, distribute /modify . developers’ authors’ protection, GPL clearly explains warranty free software. users’ authors’ sake, GPL requires modified versions marked changed, problems attributed erroneously authors previous versions. devices designed deny users access install run modified versions software inside , although manufacturer can . fundamentally incompatible aim protecting users’ freedom change software. systematic pattern abuse occurs area products individuals use, precisely unacceptable. Therefore, designed version GPL prohibit practice products. problems arise substantially domains, stand ready extend provision domains future versions GPL, needed protect freedom users. Finally, every program threatened constantly software patents. 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Termination","title":"GNU General Public License","text":"may propagate modify covered work except expressly provided License. attempt otherwise propagate modify void, automatically terminate rights License (including patent licenses granted third paragraph section 11). However, cease violation License, license particular copyright holder reinstated () provisionally, unless copyright holder explicitly finally terminates license, (b) permanently, copyright holder fails notify violation reasonable means prior 60 days cessation. Moreover, license particular copyright holder reinstated permanently copyright holder notifies violation reasonable means, first time received notice violation License (work) copyright holder, cure violation prior 30 days receipt notice. 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Interpretation of Sections 15 and 16","title":"GNU General Public License","text":"disclaimer warranty limitation liability provided given local legal effect according terms, reviewing courts shall apply local law closely approximates absolute waiver civil liability connection Program, unless warranty assumption liability accompanies copy Program return fee. END TERMS CONDITIONS","code":""},{"path":"https://astamm.github.io/nevada/LICENSE.html","id":"how-to-apply-these-terms-to-your-new-programs","dir":"","previous_headings":"","what":"How to Apply These Terms to Your New Programs","title":"GNU General Public License","text":"develop new program, want greatest possible use public, best way achieve make free software everyone can redistribute change terms. , attach following notices program. safest attach start source file effectively state exclusion warranty; file least “copyright” line pointer full notice found. Also add information contact electronic paper mail. program terminal interaction, make output short notice like starts interactive mode: hypothetical commands show w show c show appropriate parts General Public License. course, program’s commands might different; GUI interface, use “box”. also get employer (work programmer) school, , sign “copyright disclaimer” program, necessary. information , apply follow GNU GPL, see . GNU General Public License permit incorporating program proprietary programs. program subroutine library, may consider useful permit linking proprietary applications library. want , use GNU Lesser General Public License instead License. first, please read .","code":" Copyright (C) This program is free software: you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation, either version 3 of the License, or (at your option) any later version. This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with this program. If not, see . Copyright (C) This program comes with ABSOLUTELY NO WARRANTY; for details type 'show w'. This is free software, and you are welcome to redistribute it under certain conditions; type 'show c' for details."},{"path":"https://astamm.github.io/nevada/articles/nevada.html","id":"the-nvd-class-for-network-valued-data","dir":"Articles","previous_headings":"","what":"The nvd class for network-valued data","title":"nevada","text":"nevada, network-valued data stored object class nvd, basically list igraph objects. provide: constructor nvd() allows user simulate samples networks using popular models igraph. Currently, one can use: stochastic block model, kk-regular model, GNP model, small-world model, PA model, Poisson model, binomial model. constructor simulates networks 25 nodes. function as_nvd() coerce lists igraph objects object class nvd.","code":""},{"path":"https://astamm.github.io/nevada/articles/nevada.html","id":"network-representation","dir":"Articles","previous_headings":"","what":"Network representation","title":"nevada","text":"currently 3 possible matrix representations network. Let GG network NN nodes. NN x NN matrix WW adjacency matrix GG element WijW_{ij} indicates edge vertex ii vertex jj: Wij={wi,j,(,j)∈E weight wi,j0,otherwise. W_{ij}= \\begin{cases} w_{,j}, & \\mbox{} (,j) \\E \\mbox{ weight } w_{,j}\\\\ 0, & \\mbox{otherwise.} \\end{cases} nevada, representation can achieved repr_adjacency(). Laplacian matrix LL network GG defined following way: L=D(W)−W, L = D(W) - W, D(W)D(W) diagonal matrix whose ii-th diagonal element degree vertex ii. nevada, representation can achieved repr_laplacian(). elements modularity matrix BB given Bij=Wij−didj2m, B_{ij} = W_{ij} - \\frac{d_i d_j}{2m}, did_i djd_j degrees vertices ii jj respectively, mm total number edges network. nevada, representation can achieved repr_modularity(). Instead going every single network sample make representation, nevada provides repr_nvd() function exactly object class nvd.","code":"x <- nvd(sample_size = 3L, model = \"gnp\", n = 24L, p = 1/3) #> ℹ Calling the `tidygraph::play_gnp()` function with the following arguments: #> • n: 24 #> • p: 0.333333333333333 #> • directed: TRUE #> • loops: FALSE repr_nvd(x, representation = \"laplacian\") #> [[1]] #> [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12] [,13] #> [1,] 7 -1 0 -1 -1 0 0 0 -1 0 0 0 0 #> [2,] 0 5 0 -1 0 0 0 0 0 -1 -1 0 -1 #> [3,] 0 -1 8 0 0 0 -1 0 -1 -1 0 0 -1 #> [4,] 0 0 0 2 -1 0 0 0 0 0 0 0 0 #> [5,] 0 0 0 -1 8 0 0 0 -1 -1 0 0 -1 #> [6,] 0 0 -1 0 -1 7 0 0 -1 0 0 0 0 #> [7,] 0 0 0 0 0 0 6 0 0 0 0 -1 0 #> [8,] -1 0 -1 0 0 0 -1 7 0 -1 -1 0 0 #> [9,] 0 0 0 0 0 -1 0 0 10 0 0 -1 -1 #> [10,] -1 -1 -1 0 0 0 -1 -1 0 11 -1 0 0 #> [11,] 0 -1 -1 0 0 0 0 0 0 0 7 0 0 #> [12,] -1 0 0 0 -1 0 0 0 0 0 0 6 -1 #> [13,] 0 -1 0 0 0 -1 -1 0 0 0 0 -1 6 #> [14,] -1 -1 0 0 0 -1 0 0 0 0 0 -1 0 #> [15,] 0 0 -1 -1 -1 0 -1 -1 0 0 0 -1 -1 #> [16,] 0 0 -1 0 -1 0 0 0 -1 0 0 -1 0 #> [17,] 0 0 0 -1 0 -1 -1 0 0 0 -1 0 0 #> [18,] -1 -1 0 0 -1 0 0 0 0 0 0 -1 0 #> [19,] -1 -1 0 0 -1 -1 0 0 -1 0 0 0 -1 #> [20,] -1 0 0 -1 0 0 0 0 -1 0 0 0 0 #> [21,] 0 0 0 -1 -1 0 -1 -1 -1 0 0 0 -1 #> [22,] 0 0 -1 -1 0 0 0 -1 0 0 0 0 -1 #> [23,] 0 0 0 0 0 0 0 0 0 0 0 0 -1 #> [24,] 0 -1 -1 -1 0 0 -1 0 0 -1 -1 0 -1 #> [,14] [,15] [,16] [,17] [,18] [,19] [,20] [,21] [,22] [,23] [,24] #> [1,] 0 0 0 0 -1 -1 -1 0 0 0 0 #> [2,] 0 0 -1 0 0 0 0 0 0 0 0 #> [3,] 0 0 -1 0 -1 0 0 0 0 0 -1 #> [4,] 0 0 0 0 0 0 0 0 -1 0 0 #> [5,] 0 0 -1 0 -1 -1 0 -1 0 0 0 #> [6,] -1 0 0 -1 0 0 0 -1 0 -1 0 #> [7,] -1 0 0 -1 -1 0 -1 0 0 -1 0 #> [8,] 0 0 0 0 0 0 0 -1 0 0 -1 #> [9,] -1 -1 -1 -1 0 -1 -1 0 -1 0 0 #> [10,] 0 -1 -1 -1 0 -1 -1 0 0 0 0 #> [11,] 0 -1 0 -1 -1 -1 0 0 -1 0 0 #> [12,] 0 0 -1 0 0 0 -1 0 -1 0 0 #> [13,] 0 0 -1 0 0 0 0 -1 0 0 0 #> [14,] 6 0 0 0 -1 -1 0 0 0 0 0 #> [15,] 0 7 0 0 0 0 0 0 0 0 0 #> [16,] -1 0 7 0 0 0 0 -1 0 0 -1 #> [17,] 0 0 -1 9 -1 -1 -1 0 -1 0 0 #> [18,] 0 0 -1 -1 11 -1 0 -1 -1 -1 -1 #> [19,] 0 0 -1 0 0 8 -1 0 0 0 0 #> [20,] 0 0 0 0 0 0 4 0 0 0 -1 #> [21,] 0 -1 0 -1 0 -1 -1 12 -1 -1 0 #> [22,] 0 0 0 0 0 -1 -1 -1 8 0 -1 #> [23,] 0 -1 -1 0 -1 0 -1 0 0 6 -1 #> [24,] 0 0 -1 0 0 0 -1 0 0 0 9 #> attr(,\"representation\") #> [1] \"laplacian\" #> #> [[2]] #> [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12] [,13] #> [1,] 11 0 -1 0 0 -1 0 0 -1 0 -1 -1 0 #> [2,] 0 8 0 -1 0 0 -1 -1 -1 0 0 -1 0 #> [3,] 0 0 6 0 -1 0 -1 0 0 -1 0 0 0 #> [4,] -1 0 0 8 0 -1 0 -1 -1 -1 0 0 -1 #> [5,] 0 -1 -1 -1 5 0 0 0 0 0 0 0 -1 #> [6,] -1 0 -1 0 0 10 0 0 -1 0 0 0 0 #> [7,] 0 0 0 0 0 -1 6 0 -1 0 0 -1 -1 #> [8,] 0 -1 -1 0 0 -1 0 8 0 0 0 -1 0 #> [9,] 0 -1 0 -1 0 0 0 0 6 0 0 0 0 #> [10,] 0 0 0 0 0 -1 -1 -1 -1 9 0 0 -1 #> [11,] 0 -1 -1 -1 0 -1 0 -1 0 0 10 0 0 #> [12,] -1 0 0 -1 -1 0 0 -1 0 0 0 8 0 #> [13,] 0 0 0 0 -1 0 -1 -1 0 -1 0 0 9 #> [14,] 0 -1 0 0 -1 0 0 -1 0 -1 0 0 -1 #> [15,] 0 0 -1 0 0 0 0 -1 0 0 0 0 0 #> [16,] 0 0 0 -1 0 0 0 -1 0 0 0 0 0 #> [17,] -1 0 -1 0 0 0 0 0 0 -1 -1 0 -1 #> [18,] -1 0 0 -1 0 0 0 0 0 -1 0 -1 0 #> [19,] 0 0 0 0 -1 0 0 0 0 0 0 0 -1 #> [20,] -1 0 0 0 0 0 0 0 0 -1 0 0 0 #> [21,] 0 0 0 0 0 0 0 0 0 0 0 0 0 #> [22,] 0 -1 -1 -1 -1 0 0 0 0 0 0 0 0 #> [23,] 0 0 -1 -1 0 0 0 0 -1 0 0 0 0 #> [24,] -1 0 0 -1 -1 -1 0 0 -1 -1 0 0 0 #> [,14] [,15] [,16] [,17] [,18] [,19] [,20] [,21] [,22] [,23] [,24] #> [1,] 0 0 -1 0 -1 -1 -1 -1 -1 0 0 #> [2,] 0 0 -1 0 0 0 -1 0 0 0 -1 #> [3,] 0 -1 0 0 -1 -1 0 0 0 0 0 #> [4,] -1 0 0 0 0 0 0 0 0 0 -1 #> [5,] 0 0 0 0 0 0 0 -1 0 0 0 #> [6,] -1 0 -1 -1 -1 0 -1 -1 0 -1 0 #> [7,] 0 -1 0 -1 0 0 0 0 0 0 0 #> [8,] 0 0 0 0 -1 -1 0 0 -1 -1 0 #> [9,] 0 -1 -1 0 0 0 -1 0 0 -1 0 #> [10,] 0 0 0 0 0 0 -1 0 -1 -1 -1 #> [11,] 0 -1 0 0 -1 -1 -1 0 -1 0 0 #> [12,] 0 -1 0 0 0 0 -1 0 -1 -1 0 #> [13,] -1 0 0 0 -1 0 -1 0 -1 -1 0 #> [14,] 9 0 -1 0 0 0 0 -1 -1 -1 0 #> [15,] -1 5 0 0 0 0 0 -1 0 -1 0 #> [16,] 0 0 5 0 0 0 0 0 -1 -1 -1 #> [17,] 0 0 0 8 0 0 -1 -1 0 -1 0 #> [18,] 0 0 0 0 6 -1 0 -1 0 0 0 #> [19,] 0 0 0 0 0 4 0 -1 0 -1 0 #> [20,] -1 0 0 0 0 0 5 -1 -1 0 0 #> [21,] 0 0 0 -1 -1 -1 0 5 -1 -1 0 #> [22,] 0 -1 0 0 0 0 0 -1 6 0 0 #> [23,] 0 -1 0 -1 -1 -1 -1 0 0 8 0 #> [24,] 0 0 -1 0 0 -1 0 -1 -1 0 10 #> attr(,\"representation\") #> [1] \"laplacian\" #> #> [[3]] #> [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12] [,13] #> [1,] 8 -1 0 0 -1 0 0 0 -1 0 0 0 -1 #> [2,] 0 9 -1 -1 0 -1 0 0 -1 -1 -1 -1 0 #> [3,] 0 0 4 0 0 0 0 0 -1 0 0 0 -1 #> [4,] 0 -1 -1 9 0 0 -1 0 -1 0 0 0 -1 #> [5,] -1 0 0 -1 10 -1 0 -1 -1 -1 0 -1 0 #> [6,] 0 0 0 -1 -1 9 0 -1 0 0 0 0 -1 #> [7,] 0 0 0 0 -1 -1 7 0 0 -1 -1 0 0 #> [8,] -1 0 -1 0 -1 -1 0 11 -1 0 -1 0 -1 #> [9,] 0 0 0 0 0 0 0 0 4 0 -1 -1 0 #> [10,] 0 -1 0 0 0 0 0 0 -1 6 0 0 0 #> [11,] 0 0 0 -1 0 -1 -1 0 -1 -1 10 0 0 #> [12,] -1 0 -1 -1 -1 -1 0 0 -1 0 0 9 -1 #> [13,] 0 0 -1 -1 -1 -1 0 0 -1 0 -1 -1 13 #> [14,] -1 -1 -1 0 0 0 0 0 0 0 0 0 -1 #> [15,] -1 0 0 0 0 0 0 0 0 0 -1 0 0 #> [16,] 0 -1 0 0 -1 -1 0 0 0 0 0 0 0 #> [17,] 0 0 0 0 0 0 -1 0 0 0 -1 -1 0 #> [18,] -1 -1 -1 0 -1 0 0 -1 0 0 -1 -1 -1 #> [19,] 0 -1 0 0 0 -1 0 0 0 0 0 -1 -1 #> [20,] 0 -1 -1 0 0 0 0 -1 0 -1 0 -1 -1 #> [21,] 0 0 0 -1 -1 0 -1 -1 -1 -1 0 0 0 #> [22,] 0 -1 -1 0 0 0 0 0 -1 0 0 0 0 #> [23,] -1 -1 0 -1 0 -1 -1 -1 0 0 -1 0 0 #> [24,] 0 0 0 0 0 0 -1 -1 0 -1 0 0 0 #> [,14] [,15] [,16] [,17] [,18] [,19] [,20] [,21] [,22] [,23] [,24] #> [1,] -1 0 0 0 -1 0 0 -1 0 0 -1 #> [2,] 0 0 0 0 0 -1 0 0 -1 0 0 #> [3,] 0 -1 0 0 0 0 0 -1 0 0 0 #> [4,] 0 0 -1 -1 0 0 0 0 -1 0 -1 #> [5,] 0 -1 0 -1 0 0 0 0 0 -1 0 #> [6,] -1 0 -1 0 -1 0 -1 0 -1 0 0 #> [7,] 0 -1 0 0 0 0 0 0 -1 0 -1 #> [8,] 0 -1 0 0 0 0 0 -1 -1 0 -1 #> [9,] 0 -1 0 0 0 0 0 0 0 0 -1 #> [10,] 0 0 0 0 0 -1 0 0 -1 -1 -1 #> [11,] 0 0 -1 -1 0 0 -1 0 -1 0 -1 #> [12,] 0 0 0 -1 0 -1 0 0 0 0 0 #> [13,] 0 0 -1 -1 -1 -1 -1 0 0 0 -1 #> [14,] 7 -1 -1 0 0 -1 0 0 0 0 0 #> [15,] -1 8 -1 -1 -1 0 0 0 0 -1 -1 #> [16,] -1 -1 7 0 -1 0 0 -1 0 0 0 #> [17,] -1 0 -1 7 0 -1 -1 0 0 0 0 #> [18,] 0 -1 0 -1 12 -1 -1 0 0 0 0 #> [19,] 0 -1 0 -1 -1 9 -1 0 -1 0 0 #> [20,] 0 -1 0 0 0 0 8 0 0 -1 0 #> [21,] 0 -1 0 -1 -1 0 -1 11 -1 0 0 #> [22,] -1 -1 -1 0 -1 0 -1 -1 9 0 0 #> [23,] 0 0 0 -1 0 -1 -1 0 0 11 -1 #> [24,] 0 -1 0 -1 0 0 0 0 0 0 5 #> attr(,\"representation\") #> [1] \"laplacian\""},{"path":"https://astamm.github.io/nevada/articles/nevada.html","id":"adjacency-matrix","dir":"Articles","previous_headings":"","what":"Adjacency matrix","title":"nevada","text":"NN x NN matrix WW adjacency matrix GG element WijW_{ij} indicates edge vertex ii vertex jj: Wij={wi,j,(,j)∈E weight wi,j0,otherwise. W_{ij}= \\begin{cases} w_{,j}, & \\mbox{} (,j) \\E \\mbox{ weight } w_{,j}\\\\ 0, & \\mbox{otherwise.} \\end{cases} nevada, representation can achieved repr_adjacency().","code":""},{"path":"https://astamm.github.io/nevada/articles/nevada.html","id":"laplacian-matrix","dir":"Articles","previous_headings":"","what":"Laplacian matrix","title":"nevada","text":"Laplacian matrix LL network GG defined following way: L=D(W)−W, L = D(W) - W, D(W)D(W) diagonal matrix whose ii-th diagonal element degree vertex ii. nevada, representation can achieved repr_laplacian().","code":""},{"path":"https://astamm.github.io/nevada/articles/nevada.html","id":"modularity-matrix","dir":"Articles","previous_headings":"","what":"Modularity matrix","title":"nevada","text":"elements modularity matrix BB given Bij=Wij−didj2m, B_{ij} = W_{ij} - \\frac{d_i d_j}{2m}, did_i djd_j degrees vertices ii jj respectively, mm total number edges network. nevada, representation can achieved repr_modularity().","code":""},{"path":"https://astamm.github.io/nevada/articles/nevada.html","id":"choosing-a-representation-for-an-object-of-class-nvd","dir":"Articles","previous_headings":"","what":"Choosing a representation for an object of class nvd","title":"nevada","text":"Instead going every single network sample make representation, nevada provides repr_nvd() function exactly object class nvd.","code":"x <- nvd(sample_size = 3L, model = \"gnp\", n = 24L, p = 1/3) #> ℹ Calling the `tidygraph::play_gnp()` function with the following arguments: #> • n: 24 #> • p: 0.333333333333333 #> • directed: TRUE #> • loops: FALSE repr_nvd(x, representation = \"laplacian\") #> [[1]] #> [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12] [,13] #> [1,] 7 -1 0 -1 -1 0 0 0 -1 0 0 0 0 #> [2,] 0 5 0 -1 0 0 0 0 0 -1 -1 0 -1 #> [3,] 0 -1 8 0 0 0 -1 0 -1 -1 0 0 -1 #> [4,] 0 0 0 2 -1 0 0 0 0 0 0 0 0 #> [5,] 0 0 0 -1 8 0 0 0 -1 -1 0 0 -1 #> [6,] 0 0 -1 0 -1 7 0 0 -1 0 0 0 0 #> [7,] 0 0 0 0 0 0 6 0 0 0 0 -1 0 #> [8,] -1 0 -1 0 0 0 -1 7 0 -1 -1 0 0 #> [9,] 0 0 0 0 0 -1 0 0 10 0 0 -1 -1 #> [10,] -1 -1 -1 0 0 0 -1 -1 0 11 -1 0 0 #> [11,] 0 -1 -1 0 0 0 0 0 0 0 7 0 0 #> [12,] -1 0 0 0 -1 0 0 0 0 0 0 6 -1 #> [13,] 0 -1 0 0 0 -1 -1 0 0 0 0 -1 6 #> [14,] -1 -1 0 0 0 -1 0 0 0 0 0 -1 0 #> [15,] 0 0 -1 -1 -1 0 -1 -1 0 0 0 -1 -1 #> [16,] 0 0 -1 0 -1 0 0 0 -1 0 0 -1 0 #> [17,] 0 0 0 -1 0 -1 -1 0 0 0 -1 0 0 #> [18,] -1 -1 0 0 -1 0 0 0 0 0 0 -1 0 #> [19,] -1 -1 0 0 -1 -1 0 0 -1 0 0 0 -1 #> [20,] -1 0 0 -1 0 0 0 0 -1 0 0 0 0 #> [21,] 0 0 0 -1 -1 0 -1 -1 -1 0 0 0 -1 #> [22,] 0 0 -1 -1 0 0 0 -1 0 0 0 0 -1 #> [23,] 0 0 0 0 0 0 0 0 0 0 0 0 -1 #> [24,] 0 -1 -1 -1 0 0 -1 0 0 -1 -1 0 -1 #> [,14] [,15] [,16] [,17] [,18] [,19] [,20] [,21] [,22] [,23] [,24] #> [1,] 0 0 0 0 -1 -1 -1 0 0 0 0 #> [2,] 0 0 -1 0 0 0 0 0 0 0 0 #> [3,] 0 0 -1 0 -1 0 0 0 0 0 -1 #> [4,] 0 0 0 0 0 0 0 0 -1 0 0 #> [5,] 0 0 -1 0 -1 -1 0 -1 0 0 0 #> [6,] -1 0 0 -1 0 0 0 -1 0 -1 0 #> [7,] -1 0 0 -1 -1 0 -1 0 0 -1 0 #> [8,] 0 0 0 0 0 0 0 -1 0 0 -1 #> [9,] -1 -1 -1 -1 0 -1 -1 0 -1 0 0 #> [10,] 0 -1 -1 -1 0 -1 -1 0 0 0 0 #> [11,] 0 -1 0 -1 -1 -1 0 0 -1 0 0 #> [12,] 0 0 -1 0 0 0 -1 0 -1 0 0 #> [13,] 0 0 -1 0 0 0 0 -1 0 0 0 #> [14,] 6 0 0 0 -1 -1 0 0 0 0 0 #> [15,] 0 7 0 0 0 0 0 0 0 0 0 #> [16,] -1 0 7 0 0 0 0 -1 0 0 -1 #> [17,] 0 0 -1 9 -1 -1 -1 0 -1 0 0 #> [18,] 0 0 -1 -1 11 -1 0 -1 -1 -1 -1 #> [19,] 0 0 -1 0 0 8 -1 0 0 0 0 #> [20,] 0 0 0 0 0 0 4 0 0 0 -1 #> [21,] 0 -1 0 -1 0 -1 -1 12 -1 -1 0 #> [22,] 0 0 0 0 0 -1 -1 -1 8 0 -1 #> [23,] 0 -1 -1 0 -1 0 -1 0 0 6 -1 #> [24,] 0 0 -1 0 0 0 -1 0 0 0 9 #> attr(,\"representation\") #> [1] \"laplacian\" #> #> [[2]] #> [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12] [,13] #> [1,] 11 0 -1 0 0 -1 0 0 -1 0 -1 -1 0 #> [2,] 0 8 0 -1 0 0 -1 -1 -1 0 0 -1 0 #> [3,] 0 0 6 0 -1 0 -1 0 0 -1 0 0 0 #> [4,] -1 0 0 8 0 -1 0 -1 -1 -1 0 0 -1 #> [5,] 0 -1 -1 -1 5 0 0 0 0 0 0 0 -1 #> [6,] -1 0 -1 0 0 10 0 0 -1 0 0 0 0 #> [7,] 0 0 0 0 0 -1 6 0 -1 0 0 -1 -1 #> [8,] 0 -1 -1 0 0 -1 0 8 0 0 0 -1 0 #> [9,] 0 -1 0 -1 0 0 0 0 6 0 0 0 0 #> [10,] 0 0 0 0 0 -1 -1 -1 -1 9 0 0 -1 #> [11,] 0 -1 -1 -1 0 -1 0 -1 0 0 10 0 0 #> [12,] -1 0 0 -1 -1 0 0 -1 0 0 0 8 0 #> [13,] 0 0 0 0 -1 0 -1 -1 0 -1 0 0 9 #> [14,] 0 -1 0 0 -1 0 0 -1 0 -1 0 0 -1 #> [15,] 0 0 -1 0 0 0 0 -1 0 0 0 0 0 #> [16,] 0 0 0 -1 0 0 0 -1 0 0 0 0 0 #> [17,] -1 0 -1 0 0 0 0 0 0 -1 -1 0 -1 #> [18,] -1 0 0 -1 0 0 0 0 0 -1 0 -1 0 #> [19,] 0 0 0 0 -1 0 0 0 0 0 0 0 -1 #> [20,] -1 0 0 0 0 0 0 0 0 -1 0 0 0 #> [21,] 0 0 0 0 0 0 0 0 0 0 0 0 0 #> [22,] 0 -1 -1 -1 -1 0 0 0 0 0 0 0 0 #> [23,] 0 0 -1 -1 0 0 0 0 -1 0 0 0 0 #> [24,] -1 0 0 -1 -1 -1 0 0 -1 -1 0 0 0 #> [,14] [,15] [,16] [,17] [,18] [,19] [,20] [,21] [,22] [,23] [,24] #> [1,] 0 0 -1 0 -1 -1 -1 -1 -1 0 0 #> [2,] 0 0 -1 0 0 0 -1 0 0 0 -1 #> [3,] 0 -1 0 0 -1 -1 0 0 0 0 0 #> [4,] -1 0 0 0 0 0 0 0 0 0 -1 #> [5,] 0 0 0 0 0 0 0 -1 0 0 0 #> [6,] -1 0 -1 -1 -1 0 -1 -1 0 -1 0 #> [7,] 0 -1 0 -1 0 0 0 0 0 0 0 #> [8,] 0 0 0 0 -1 -1 0 0 -1 -1 0 #> [9,] 0 -1 -1 0 0 0 -1 0 0 -1 0 #> [10,] 0 0 0 0 0 0 -1 0 -1 -1 -1 #> [11,] 0 -1 0 0 -1 -1 -1 0 -1 0 0 #> [12,] 0 -1 0 0 0 0 -1 0 -1 -1 0 #> [13,] -1 0 0 0 -1 0 -1 0 -1 -1 0 #> [14,] 9 0 -1 0 0 0 0 -1 -1 -1 0 #> [15,] -1 5 0 0 0 0 0 -1 0 -1 0 #> [16,] 0 0 5 0 0 0 0 0 -1 -1 -1 #> [17,] 0 0 0 8 0 0 -1 -1 0 -1 0 #> [18,] 0 0 0 0 6 -1 0 -1 0 0 0 #> [19,] 0 0 0 0 0 4 0 -1 0 -1 0 #> [20,] -1 0 0 0 0 0 5 -1 -1 0 0 #> [21,] 0 0 0 -1 -1 -1 0 5 -1 -1 0 #> [22,] 0 -1 0 0 0 0 0 -1 6 0 0 #> [23,] 0 -1 0 -1 -1 -1 -1 0 0 8 0 #> [24,] 0 0 -1 0 0 -1 0 -1 -1 0 10 #> attr(,\"representation\") #> [1] \"laplacian\" #> #> [[3]] #> [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12] [,13] #> [1,] 8 -1 0 0 -1 0 0 0 -1 0 0 0 -1 #> [2,] 0 9 -1 -1 0 -1 0 0 -1 -1 -1 -1 0 #> [3,] 0 0 4 0 0 0 0 0 -1 0 0 0 -1 #> [4,] 0 -1 -1 9 0 0 -1 0 -1 0 0 0 -1 #> [5,] -1 0 0 -1 10 -1 0 -1 -1 -1 0 -1 0 #> [6,] 0 0 0 -1 -1 9 0 -1 0 0 0 0 -1 #> [7,] 0 0 0 0 -1 -1 7 0 0 -1 -1 0 0 #> [8,] -1 0 -1 0 -1 -1 0 11 -1 0 -1 0 -1 #> [9,] 0 0 0 0 0 0 0 0 4 0 -1 -1 0 #> [10,] 0 -1 0 0 0 0 0 0 -1 6 0 0 0 #> [11,] 0 0 0 -1 0 -1 -1 0 -1 -1 10 0 0 #> [12,] -1 0 -1 -1 -1 -1 0 0 -1 0 0 9 -1 #> [13,] 0 0 -1 -1 -1 -1 0 0 -1 0 -1 -1 13 #> [14,] -1 -1 -1 0 0 0 0 0 0 0 0 0 -1 #> [15,] -1 0 0 0 0 0 0 0 0 0 -1 0 0 #> [16,] 0 -1 0 0 -1 -1 0 0 0 0 0 0 0 #> [17,] 0 0 0 0 0 0 -1 0 0 0 -1 -1 0 #> [18,] -1 -1 -1 0 -1 0 0 -1 0 0 -1 -1 -1 #> [19,] 0 -1 0 0 0 -1 0 0 0 0 0 -1 -1 #> [20,] 0 -1 -1 0 0 0 0 -1 0 -1 0 -1 -1 #> [21,] 0 0 0 -1 -1 0 -1 -1 -1 -1 0 0 0 #> [22,] 0 -1 -1 0 0 0 0 0 -1 0 0 0 0 #> [23,] -1 -1 0 -1 0 -1 -1 -1 0 0 -1 0 0 #> [24,] 0 0 0 0 0 0 -1 -1 0 -1 0 0 0 #> [,14] [,15] [,16] [,17] [,18] [,19] [,20] [,21] [,22] [,23] [,24] #> [1,] -1 0 0 0 -1 0 0 -1 0 0 -1 #> [2,] 0 0 0 0 0 -1 0 0 -1 0 0 #> [3,] 0 -1 0 0 0 0 0 -1 0 0 0 #> [4,] 0 0 -1 -1 0 0 0 0 -1 0 -1 #> [5,] 0 -1 0 -1 0 0 0 0 0 -1 0 #> [6,] -1 0 -1 0 -1 0 -1 0 -1 0 0 #> [7,] 0 -1 0 0 0 0 0 0 -1 0 -1 #> [8,] 0 -1 0 0 0 0 0 -1 -1 0 -1 #> [9,] 0 -1 0 0 0 0 0 0 0 0 -1 #> [10,] 0 0 0 0 0 -1 0 0 -1 -1 -1 #> [11,] 0 0 -1 -1 0 0 -1 0 -1 0 -1 #> [12,] 0 0 0 -1 0 -1 0 0 0 0 0 #> [13,] 0 0 -1 -1 -1 -1 -1 0 0 0 -1 #> [14,] 7 -1 -1 0 0 -1 0 0 0 0 0 #> [15,] -1 8 -1 -1 -1 0 0 0 0 -1 -1 #> [16,] -1 -1 7 0 -1 0 0 -1 0 0 0 #> [17,] -1 0 -1 7 0 -1 -1 0 0 0 0 #> [18,] 0 -1 0 -1 12 -1 -1 0 0 0 0 #> [19,] 0 -1 0 -1 -1 9 -1 0 -1 0 0 #> [20,] 0 -1 0 0 0 0 8 0 0 -1 0 #> [21,] 0 -1 0 -1 -1 0 -1 11 -1 0 0 #> [22,] -1 -1 -1 0 -1 0 -1 -1 9 0 0 #> [23,] 0 0 0 -1 0 -1 -1 0 0 11 -1 #> [24,] 0 -1 0 -1 0 0 0 0 0 0 5 #> attr(,\"representation\") #> [1] \"laplacian\""},{"path":"https://astamm.github.io/nevada/articles/nevada.html","id":"distances-between-networks","dir":"Articles","previous_headings":"","what":"Distances between networks","title":"nevada","text":"possible choose distance consider analysis. Let GG HH two networks NN nodes suppose XX YY matrix representations GG HH, respectively. user can currently choose among 4 distances: Hamming, Frobenius, spectral root-Euclidean. $$ \\rho_H(G,H)=\\frac{1}{N(N-1)}\\sum_{\\neq j}^N \\bigl\\arrowvert X_{,j}-Y_{,j} \\bigr\\arrowvert. $$ nevada, distance can computed dist_hamming(). ρF(G,H)=∥X−Y∥F2=∑≠jN(Xi,j−Yi,j)2. \\rho_F(G,H) = \\left\\| X - Y \\right\\|_F^2 = \\sum_{\\neq j}^N \\bigl ( X_{,j}-Y_{,j} \\bigr )^2. nevada, distance can computed dist_frobenius(). ρS(G,H)=∑≠jN(Λi,jX−Λi,jY)2, \\rho_S(G,H)=\\sum_{\\neq j}^N \\bigl ( \\Lambda^X_{,j}-\\Lambda^Y_{,j} \\bigr )^2, ΛX\\Lambda^X ΛY\\Lambda^Y diagonal matrices eigenvalues diagonal given spectral decomposition matrix representations GG HH. nevada, distance can computed dist_spectral(). ρRE(G,H)=∥X1/2−Y1/2∥F2. \\rho_{RE}(G,H) = \\left\\| X^{1/2} - Y^{1/2} \\right\\|_F^2. Note distance compatible matrix representations requires representation semi-positive definite. nevada, distance can computed dist_root_euclidean(). Pre-computation matrix pairwise distances samples networks alleviates computational burden permutation testing. nevada provides convenient dist_nvd() function exactly object class nvd.","code":"x <- nvd(sample_size = 3L, model = \"gnp\", n = 24L, p = 1/3) #> ℹ Calling the `tidygraph::play_gnp()` function with the following arguments: #> • n: 24 #> • p: 0.333333333333333 #> • directed: TRUE #> • loops: FALSE dist_nvd(x, representation = \"laplacian\", distance = \"hamming\") #> 1 2 #> 2 0.5760870 #> 3 0.5271739 0.5307971"},{"path":"https://astamm.github.io/nevada/articles/nevada.html","id":"hamming-distance","dir":"Articles","previous_headings":"","what":"Hamming distance","title":"nevada","text":"$$ \\rho_H(G,H)=\\frac{1}{N(N-1)}\\sum_{\\neq j}^N \\bigl\\arrowvert X_{,j}-Y_{,j} \\bigr\\arrowvert. $$ nevada, distance can computed dist_hamming().","code":""},{"path":"https://astamm.github.io/nevada/articles/nevada.html","id":"frobenius-distance","dir":"Articles","previous_headings":"","what":"Frobenius distance","title":"nevada","text":"ρF(G,H)=∥X−Y∥F2=∑≠jN(Xi,j−Yi,j)2. \\rho_F(G,H) = \\left\\| X - Y \\right\\|_F^2 = \\sum_{\\neq j}^N \\bigl ( X_{,j}-Y_{,j} \\bigr )^2. nevada, distance can computed dist_frobenius().","code":""},{"path":"https://astamm.github.io/nevada/articles/nevada.html","id":"spectral-distance","dir":"Articles","previous_headings":"","what":"Spectral distance","title":"nevada","text":"ρS(G,H)=∑≠jN(Λi,jX−Λi,jY)2, \\rho_S(G,H)=\\sum_{\\neq j}^N \\bigl ( \\Lambda^X_{,j}-\\Lambda^Y_{,j} \\bigr )^2, ΛX\\Lambda^X ΛY\\Lambda^Y diagonal matrices eigenvalues diagonal given spectral decomposition matrix representations GG HH. nevada, distance can computed dist_spectral().","code":""},{"path":"https://astamm.github.io/nevada/articles/nevada.html","id":"root-euclidean-distance","dir":"Articles","previous_headings":"","what":"Root Euclidean distance","title":"nevada","text":"ρRE(G,H)=∥X1/2−Y1/2∥F2. \\rho_{RE}(G,H) = \\left\\| X^{1/2} - Y^{1/2} \\right\\|_F^2. Note distance compatible matrix representations requires representation semi-positive definite. nevada, distance can computed dist_root_euclidean().","code":""},{"path":"https://astamm.github.io/nevada/articles/nevada.html","id":"computing-a-matrix-of-pairwise-distances-for-an-object-of-class-nvd","dir":"Articles","previous_headings":"","what":"Computing a matrix of pairwise distances for an object of class nvd","title":"nevada","text":"Pre-computation matrix pairwise distances samples networks alleviates computational burden permutation testing. nevada provides convenient dist_nvd() function exactly object class nvd.","code":"x <- nvd(sample_size = 3L, model = \"gnp\", n = 24L, p = 1/3) #> ℹ Calling the `tidygraph::play_gnp()` function with the following arguments: #> • n: 24 #> • p: 0.333333333333333 #> • directed: TRUE #> • loops: FALSE dist_nvd(x, representation = \"laplacian\", distance = \"hamming\") #> 1 2 #> 2 0.5760870 #> 3 0.5271739 0.5307971"},{"path":"https://astamm.github.io/nevada/articles/nevada.html","id":"test-statistics","dir":"Articles","previous_headings":"","what":"Test statistics","title":"nevada","text":"nevada package designed work well flipr package, handles permutation scheme suitable representation, distance test statistics chosen. efficient way two-sample testing network-valued data pertains use statistics based inter-point distances, pairwise distances observations. number test statistics along line proposed literature, including (Lovato et al. 2020). test statistics rely inter-point distances, specific network-valued data. , can found flipr. adopt naming convention test statistic function shall start prefix stat_. statistics based inter-point distances named suffix _ip. list test statistics based inter-point distances currently available flipr: stat_student_ip() alias stat_t_ip() implement Student-like test statistic based inter-point distances proposed Lovato et al. (2020); stat_fisher_ip() alias stat_f_ip() implement Fisher-like test statistic based inter-point distances proposed Lovato et al. (2020); stat_bg_ip() implements statistic proposed Biswas Ghosh (2014); stat_energy_ip() implements class energy-based statistics proposed Székely Rizzo (2013); stat_cq_ip() implements statistic proposed S. X. Chen Qin (2010); stat_mod_ip() implements statistic computes mean inter-point distances; stat_dom_ip() implements statistic computes distance medoids two samples, possibly standardized pooled corresponding variances. also 3 statistics proposed H. Chen, Chen, Su (2018) based similarity graph built top distance matrix: stat_original_edge_count(), stat_generalized_edge_count(), stat_weighted_edge_count(). also Student-like statistics available Frobenius distance can easily compute Fréchet mean. : stat_student_euclidean(), stat_welch_euclidean(). addition test statistic functions already implemented flipr nevada, can also implement function. Test statistic functions compatible flipr least two mandatory input arguments: data either concatenated list size nx+nyn_x + n_y regrouping data points samples distance matrix size (nx+ny)×(nx+ny)(n_x + n_y) \\times (n_x + n_y) stored object class dist. indices1 integer vector size nxn_x storing indices data points belonging first sample current permuted version data. flipr package provides helper function use_stat(nsamples = 2, stat_name = ) makes easy users create test statistic ready used nevada. function creates saves .R file R/ folder current working directory populates following template: instance, flipr-compatible version tt-statistic pooled variance look like: Test statistics passed functions test2_global() test2_local() via argument stats accepts character vector : statistics nevada expected named without stat_ prefix (e.g. \"original_edge_count\" \"student_euclidean\"). statistics flipr expected named without stat_ prefix adding flipr: prefix (e.g., \"flipr:student_ip\"). statistics package pkg expected named without stat_ prefix adding pkg: prefix. Note can also refer test statistic function nevada using naming \"nevada:original_edge_count\" test statistics flipr. mandatory instance yet loaded nevada environment via library(nevada). permutation testing, choice test statistic determines alternative hypothesis, null hypothesis always distributions generated observed samples . means use Student statistic stat_student_ip() instance, actually testing whether means distributions different. ’d rather sensitive differences variances distributions, go Fisher statistic stat_fisher_ip(). can also sensitive multiple aspects distribution testing via permutation framework. achieved hood flipr package implements -called non-parametric combination (NPC) approach proposed Pesarin Salmaso (2010) provide one test statistics stats argument. can read article know implementation flipr. bottom line , example, can choose Student Fisher statistics test simultaneously differences mean variance.","code":"#' Test Statistic for the Two-Sample Problem #' #' This function computes the test statistic... #' #' @param data A list storing the concatenation of the two samples from which #' the user wants to make inference. Alternatively, a distance matrix stored #' in an object of class \\code{\\link[stats]{dist}} of pairwise distances #' between data points. #' @param indices1 An integer vector that contains the indices of the data #' points belong to the first sample in the current permuted version of the #' data. #' #' @return A numeric value evaluating the desired test statistic. #' @export #' #' @examples #' # TO BE DONE BY THE DEVELOPER OF THE PACKAGE stat_{{{name}}} <- function(data, indices1) { n <- if (inherits(data, \"dist\")) attr(data, \"Size\") else if (inherits(data, \"list\")) length(data) else stop(\"The `data` input should be of class either list or dist.\") indices2 <- seq_len(n)[-indices1] x <- data[indices1] y <- data[indices2] # Here comes the code that computes the desired test # statistic from input samples stored in lists x and y } stat_student <- function(data, indices1) { n <- if (inherits(data, \"dist\")) attr(data, \"Size\") else if (inherits(data, \"list\")) length(data) else stop(\"The `data` input should be of class either list or dist.\") indices2 <- seq_len(n)[-indices1] x <- data[indices1] y <- data[indices2] # Here comes the code that computes the desired test # statistic from input samples stored in lists x and y x <- unlist(x) y <- unlist(y) stats::t.test(x, y, var.equal = TRUE)$statistic } x <- nvd(sample_size = 10L, model = \"gnp\", n = 24L, p = 1/3) #> ℹ Calling the `tidygraph::play_gnp()` function with the following arguments: #> • n: 24 #> • p: 0.333333333333333 #> • directed: TRUE #> • loops: FALSE y <- nvd(sample_size = 10L, model = \"degree\" , out_degree = rep(2, 24L), method = \"configuration\") #> ℹ Calling the `tidygraph::play_degree()` function with the following arguments: #> • out_degree: 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, …, 2, and 2 #> • method: configuration #> • in_degree: NULL test2_global( x = x, y = y, representation = \"laplacian\", distance = \"frobenius\", stats = c(\"flipr:student_ip\", \"flipr:fisher_ip\"), seed = 1234 )$pvalue #> [1] 0.0009962984"},{"path":"https://astamm.github.io/nevada/articles/nevada.html","id":"available-statistics","dir":"Articles","previous_headings":"","what":"Available statistics","title":"nevada","text":"number test statistics along line proposed literature, including (Lovato et al. 2020). test statistics rely inter-point distances, specific network-valued data. , can found flipr. adopt naming convention test statistic function shall start prefix stat_. statistics based inter-point distances named suffix _ip. list test statistics based inter-point distances currently available flipr: stat_student_ip() alias stat_t_ip() implement Student-like test statistic based inter-point distances proposed Lovato et al. (2020); stat_fisher_ip() alias stat_f_ip() implement Fisher-like test statistic based inter-point distances proposed Lovato et al. (2020); stat_bg_ip() implements statistic proposed Biswas Ghosh (2014); stat_energy_ip() implements class energy-based statistics proposed Székely Rizzo (2013); stat_cq_ip() implements statistic proposed S. X. Chen Qin (2010); stat_mod_ip() implements statistic computes mean inter-point distances; stat_dom_ip() implements statistic computes distance medoids two samples, possibly standardized pooled corresponding variances. also 3 statistics proposed H. Chen, Chen, Su (2018) based similarity graph built top distance matrix: stat_original_edge_count(), stat_generalized_edge_count(), stat_weighted_edge_count(). also Student-like statistics available Frobenius distance can easily compute Fréchet mean. : stat_student_euclidean(), stat_welch_euclidean(). addition test statistic functions already implemented flipr nevada, can also implement function. Test statistic functions compatible flipr least two mandatory input arguments: data either concatenated list size nx+nyn_x + n_y regrouping data points samples distance matrix size (nx+ny)×(nx+ny)(n_x + n_y) \\times (n_x + n_y) stored object class dist. indices1 integer vector size nxn_x storing indices data points belonging first sample current permuted version data. flipr package provides helper function use_stat(nsamples = 2, stat_name = ) makes easy users create test statistic ready used nevada. function creates saves .R file R/ folder current working directory populates following template: instance, flipr-compatible version tt-statistic pooled variance look like:","code":"#' Test Statistic for the Two-Sample Problem #' #' This function computes the test statistic... #' #' @param data A list storing the concatenation of the two samples from which #' the user wants to make inference. Alternatively, a distance matrix stored #' in an object of class \\code{\\link[stats]{dist}} of pairwise distances #' between data points. #' @param indices1 An integer vector that contains the indices of the data #' points belong to the first sample in the current permuted version of the #' data. #' #' @return A numeric value evaluating the desired test statistic. #' @export #' #' @examples #' # TO BE DONE BY THE DEVELOPER OF THE PACKAGE stat_{{{name}}} <- function(data, indices1) { n <- if (inherits(data, \"dist\")) attr(data, \"Size\") else if (inherits(data, \"list\")) length(data) else stop(\"The `data` input should be of class either list or dist.\") indices2 <- seq_len(n)[-indices1] x <- data[indices1] y <- data[indices2] # Here comes the code that computes the desired test # statistic from input samples stored in lists x and y } stat_student <- function(data, indices1) { n <- if (inherits(data, \"dist\")) attr(data, \"Size\") else if (inherits(data, \"list\")) length(data) else stop(\"The `data` input should be of class either list or dist.\") indices2 <- seq_len(n)[-indices1] x <- data[indices1] y <- data[indices2] # Here comes the code that computes the desired test # statistic from input samples stored in lists x and y x <- unlist(x) y <- unlist(y) stats::t.test(x, y, var.equal = TRUE)$statistic }"},{"path":"https://astamm.github.io/nevada/articles/nevada.html","id":"from-flipr","dir":"Articles","previous_headings":"Test statistics","what":"From flipr","title":"nevada","text":"number test statistics along line proposed literature, including (Lovato et al. 2020). test statistics rely inter-point distances, specific network-valued data. , can found flipr. adopt naming convention test statistic function shall start prefix stat_. statistics based inter-point distances named suffix _ip. list test statistics based inter-point distances currently available flipr: stat_student_ip() alias stat_t_ip() implement Student-like test statistic based inter-point distances proposed Lovato et al. (2020); stat_fisher_ip() alias stat_f_ip() implement Fisher-like test statistic based inter-point distances proposed Lovato et al. (2020); stat_bg_ip() implements statistic proposed Biswas Ghosh (2014); stat_energy_ip() implements class energy-based statistics proposed Székely Rizzo (2013); stat_cq_ip() implements statistic proposed S. X. Chen Qin (2010); stat_mod_ip() implements statistic computes mean inter-point distances; stat_dom_ip() implements statistic computes distance medoids two samples, possibly standardized pooled corresponding variances.","code":""},{"path":"https://astamm.github.io/nevada/articles/nevada.html","id":"from-nevada","dir":"Articles","previous_headings":"Test statistics","what":"From nevada","title":"nevada","text":"also 3 statistics proposed H. Chen, Chen, Su (2018) based similarity graph built top distance matrix: stat_original_edge_count(), stat_generalized_edge_count(), stat_weighted_edge_count(). also Student-like statistics available Frobenius distance can easily compute Fréchet mean. : stat_student_euclidean(), stat_welch_euclidean().","code":""},{"path":"https://astamm.github.io/nevada/articles/nevada.html","id":"write-your-own-test-statistic-function","dir":"Articles","previous_headings":"Test statistics","what":"Write your own test statistic function","title":"nevada","text":"addition test statistic functions already implemented flipr nevada, can also implement function. Test statistic functions compatible flipr least two mandatory input arguments: data either concatenated list size nx+nyn_x + n_y regrouping data points samples distance matrix size (nx+ny)×(nx+ny)(n_x + n_y) \\times (n_x + n_y) stored object class dist. indices1 integer vector size nxn_x storing indices data points belonging first sample current permuted version data. flipr package provides helper function use_stat(nsamples = 2, stat_name = ) makes easy users create test statistic ready used nevada. function creates saves .R file R/ folder current working directory populates following template: instance, flipr-compatible version tt-statistic pooled variance look like:","code":"#' Test Statistic for the Two-Sample Problem #' #' This function computes the test statistic... #' #' @param data A list storing the concatenation of the two samples from which #' the user wants to make inference. Alternatively, a distance matrix stored #' in an object of class \\code{\\link[stats]{dist}} of pairwise distances #' between data points. #' @param indices1 An integer vector that contains the indices of the data #' points belong to the first sample in the current permuted version of the #' data. #' #' @return A numeric value evaluating the desired test statistic. #' @export #' #' @examples #' # TO BE DONE BY THE DEVELOPER OF THE PACKAGE stat_{{{name}}} <- function(data, indices1) { n <- if (inherits(data, \"dist\")) attr(data, \"Size\") else if (inherits(data, \"list\")) length(data) else stop(\"The `data` input should be of class either list or dist.\") indices2 <- seq_len(n)[-indices1] x <- data[indices1] y <- data[indices2] # Here comes the code that computes the desired test # statistic from input samples stored in lists x and y } stat_student <- function(data, indices1) { n <- if (inherits(data, \"dist\")) attr(data, \"Size\") else if (inherits(data, \"list\")) length(data) else stop(\"The `data` input should be of class either list or dist.\") indices2 <- seq_len(n)[-indices1] x <- data[indices1] y <- data[indices2] # Here comes the code that computes the desired test # statistic from input samples stored in lists x and y x <- unlist(x) y <- unlist(y) stats::t.test(x, y, var.equal = TRUE)$statistic }"},{"path":"https://astamm.github.io/nevada/articles/nevada.html","id":"usage","dir":"Articles","previous_headings":"","what":"Usage","title":"nevada","text":"Test statistics passed functions test2_global() test2_local() via argument stats accepts character vector : statistics nevada expected named without stat_ prefix (e.g. \"original_edge_count\" \"student_euclidean\"). statistics flipr expected named without stat_ prefix adding flipr: prefix (e.g., \"flipr:student_ip\"). statistics package pkg expected named without stat_ prefix adding pkg: prefix. Note can also refer test statistic function nevada using naming \"nevada:original_edge_count\" test statistics flipr. mandatory instance yet loaded nevada environment via library(nevada). permutation testing, choice test statistic determines alternative hypothesis, null hypothesis always distributions generated observed samples . means use Student statistic stat_student_ip() instance, actually testing whether means distributions different. ’d rather sensitive differences variances distributions, go Fisher statistic stat_fisher_ip(). can also sensitive multiple aspects distribution testing via permutation framework. achieved hood flipr package implements -called non-parametric combination (NPC) approach proposed Pesarin Salmaso (2010) provide one test statistics stats argument. can read article know implementation flipr. bottom line , example, can choose Student Fisher statistics test simultaneously differences mean variance.","code":"x <- nvd(sample_size = 10L, model = \"gnp\", n = 24L, p = 1/3) #> ℹ Calling the `tidygraph::play_gnp()` function with the following arguments: #> • n: 24 #> • p: 0.333333333333333 #> • directed: TRUE #> • loops: FALSE y <- nvd(sample_size = 10L, model = \"degree\" , out_degree = rep(2, 24L), method = \"configuration\") #> ℹ Calling the `tidygraph::play_degree()` function with the following arguments: #> • out_degree: 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, …, 2, and 2 #> • method: configuration #> • in_degree: NULL test2_global( x = x, y = y, representation = \"laplacian\", distance = \"frobenius\", stats = c(\"flipr:student_ip\", \"flipr:fisher_ip\"), seed = 1234 )$pvalue #> [1] 0.0009962984"},{"path":"https://astamm.github.io/nevada/articles/nevada.html","id":"naming-conventions","dir":"Articles","previous_headings":"Test statistics","what":"Naming conventions","title":"nevada","text":"Test statistics passed functions test2_global() test2_local() via argument stats accepts character vector : statistics nevada expected named without stat_ prefix (e.g. \"original_edge_count\" \"student_euclidean\"). statistics flipr expected named without stat_ prefix adding flipr: prefix (e.g., \"flipr:student_ip\"). statistics package pkg expected named without stat_ prefix adding pkg: prefix. Note can also refer test statistic function nevada using naming \"nevada:original_edge_count\" test statistics flipr. mandatory instance yet loaded nevada environment via library(nevada).","code":"x <- nvd(sample_size = 10L, model = \"gnp\", n = 24L, p = 1/3) #> ℹ Calling the `tidygraph::play_gnp()` function with the following arguments: #> • n: 24 #> • p: 0.333333333333333 #> • directed: TRUE #> • loops: FALSE y <- nvd(sample_size = 10L, model = \"degree\" , out_degree = rep(2, 24L), method = \"configuration\") #> ℹ Calling the `tidygraph::play_degree()` function with the following arguments: #> • out_degree: 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, …, 2, and 2 #> • method: configuration #> • in_degree: NULL test2_global( x = x, y = y, representation = \"laplacian\", distance = \"frobenius\", stats = c(\"flipr:student_ip\", \"flipr:fisher_ip\"), seed = 1234 )$pvalue #> [1] 0.0009962984"},{"path":"https://astamm.github.io/nevada/articles/nevada.html","id":"using-multiple-test-statistics","dir":"Articles","previous_headings":"Test statistics","what":"Using multiple test statistics","title":"nevada","text":"permutation testing, choice test statistic determines alternative hypothesis, null hypothesis always distributions generated observed samples . means use Student statistic stat_student_ip() instance, actually testing whether means distributions different. ’d rather sensitive differences variances distributions, go Fisher statistic stat_fisher_ip(). can also sensitive multiple aspects distribution testing via permutation framework. achieved hood flipr package implements -called non-parametric combination (NPC) approach proposed Pesarin Salmaso (2010) provide one test statistics stats argument. can read article know implementation flipr. bottom line , example, can choose Student Fisher statistics test simultaneously differences mean variance.","code":""},{"path":[]},{"path":"https://astamm.github.io/nevada/authors.html","id":null,"dir":"","previous_headings":"","what":"Authors","title":"Authors and Citation","text":"Ilenia Lovato. Author. Alessia Pini. Author. Aymeric Stamm. Author, maintainer. Simone Vantini. Author.","code":""},{"path":"https://astamm.github.io/nevada/authors.html","id":"citation","dir":"","previous_headings":"","what":"Citation","title":"Authors and Citation","text":"Lovato , Pini , Stamm , Vantini S (2024). nevada: Network-Valued Data Analysis. R package version 0.2.0.9000, https://github.com/astamm/nevada/, https://astamm.github.io/nevada/.","code":"@Manual{, title = {nevada: Network-Valued Data Analysis}, author = {Ilenia Lovato and Alessia Pini and Aymeric Stamm and Simone Vantini}, year = {2024}, note = {R package version 0.2.0.9000, https://github.com/astamm/nevada/}, url = {https://astamm.github.io/nevada/}, }"},{"path":"https://astamm.github.io/nevada/index.html","id":"overview-","dir":"","previous_headings":"","what":"Network-Valued Data Analysis","title":"Network-Valued Data Analysis","text":"package nevada (NEtwork-VAlued Data Analysis) R package statistical analysis network-valued data. setting, sample made statistical units networks . package provides set matrix representations networks network-valued data can transformed matrix-valued data. Subsequently, number distances matrices provided well quantify far two networks several test statistics proposed testing equality distribution samples networks using exact permutation testing procedures. permutation scheme carried flipr package also provides number test statistics based inter-point distances play nicely network-valued data. implementation largely made C++ matrix inter- intra-sample distances pre-computed, alleviates computational burden often associated permutation tests.","code":""},{"path":"https://astamm.github.io/nevada/index.html","id":"installation","dir":"","previous_headings":"","what":"Installation","title":"Network-Valued Data Analysis","text":"can install latest stable version nevada CRAN : can install development version GitHub :","code":"install.packages(\"nevada\") # install.packages(\"remotes\") remotes::install_github(\"astamm/nevada\")"},{"path":[]},{"path":"https://astamm.github.io/nevada/index.html","id":"example-1","dir":"","previous_headings":"Usage","what":"Example 1","title":"Network-Valued Data Analysis","text":"first example, compare two populations networks generated according two different models (Watts-Strogatz Barabasi), using adjacency matrix representation networks, Frobenius distance compare single networks combination Student-like Fisher-like statistics based inter-point distances summarize information perform permutation test. default nvd() constructor generates networks 25 nodes. One can wonder whether difference distributions generated two samples (given models used). test2_global() function provides answer question: p-value small, leading conclusion reject null hypothesis equal distributions. Although fake example, create partition try localize differences along partition: test2_local() function provides answer question:","code":"sample_size <- 10L num_vertices <- 10L smallworld_params <- list(n_dim = 1L, dim_size = num_vertices, order = 4L, p_rewire = 0.15) barabasi_albert_params <- list(power = 1L, n = num_vertices) withr::with_seed(1234, { x <- nevada::nvd( sample_size = sample_size, model = \"smallworld\", !!!smallworld_params ) y <- nevada::nvd( sample_size = sample_size, model = \"barabasi_albert\", !!!barabasi_albert_params ) }) ℹ Calling the `tidygraph::play_smallworld()` function with the following arguments: • n_dim: 1 • dim_size: 10 • order: 4 • p_rewire: 0.15 • loops: FALSE • multiple: FALSE ℹ Calling the `tidygraph::play_barabasi_albert()` function with the following arguments: • power: 1 • n: 10 • growth: 1 • growth_dist: NULL • use_out: FALSE • appeal_zero: 1 • directed: TRUE • method: psumtree t1_global <- nevada::test2_global(x, y, seed = 1234) t1_global$pvalue [1] 0.0009962984 partition <- as.integer(c(1:5, each = 5)) t1_local <- nevada::test2_local(x, y, partition, seed = 1234) t1_local $intra # A tibble: 5 × 3 E pvalue truncated 1 P1 0.425 TRUE 2 P2 0.425 TRUE 3 P3 0.425 TRUE 4 P4 0.425 TRUE 5 P5 0.425 TRUE $inter # A tibble: 10 × 4 E1 E2 pvalue truncated 1 P1 P2 0.000996 FALSE 2 P1 P3 0.000996 FALSE 3 P1 P4 0.000996 FALSE 4 P1 P5 0.000996 FALSE 5 P2 P3 0.000996 FALSE 6 P2 P4 0.000996 FALSE 7 P2 P5 0.000996 FALSE 8 P3 P4 0.000996 FALSE 9 P3 P5 0.000996 FALSE 10 P4 P5 0.000996 FALSE"},{"path":"https://astamm.github.io/nevada/index.html","id":"example-2","dir":"","previous_headings":"Usage","what":"Example 2","title":"Network-Valued Data Analysis","text":"second example, compare two populations networks generated according model (Watts-Strogatz), using adjacency matrix representation networks, Frobenius distance compare single networks combination Student-like Fisher-like statistics based inter-point distances summarize information perform permutation test. One can wonder whether difference distributions generated two samples (given models used). test2_global() function provides answer question: p-value larger 5% even 10%, leading us failing reject null hypothesis equal distributions significance thresholds.","code":"withr::with_seed(1234, { x <- nevada::nvd( sample_size = sample_size, model = \"smallworld\", !!!smallworld_params ) y <- nevada::nvd( sample_size = sample_size, model = \"smallworld\", !!!smallworld_params ) }) ℹ Calling the `tidygraph::play_smallworld()` function with the following arguments: • n_dim: 1 • dim_size: 10 • order: 4 • p_rewire: 0.15 • loops: FALSE • multiple: FALSE ℹ Calling the `tidygraph::play_smallworld()` function with the following arguments: • n_dim: 1 • dim_size: 10 • order: 4 • p_rewire: 0.15 • loops: FALSE • multiple: FALSE t2 <- nevada::test2_global(x, y, seed = 1234) t2$pvalue [1] 0.9190782"},{"path":"https://astamm.github.io/nevada/reference/as_nvd.html","id":null,"dir":"Reference","previous_headings":"","what":"Coercion to Network-Valued Data Object — as_nvd","title":"Coercion to Network-Valued Data Object — as_nvd","text":"function flags list igraph objects nvd object defined package.","code":""},{"path":"https://astamm.github.io/nevada/reference/as_nvd.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Coercion to Network-Valued Data Object — as_nvd","text":"","code":"as_nvd(obj)"},{"path":"https://astamm.github.io/nevada/reference/as_nvd.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Coercion to Network-Valued Data Object — as_nvd","text":"obj list igraph objects.","code":""},{"path":"https://astamm.github.io/nevada/reference/as_nvd.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Coercion to Network-Valued Data Object — as_nvd","text":"nvd object.","code":""},{"path":"https://astamm.github.io/nevada/reference/as_nvd.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Coercion to Network-Valued Data Object — as_nvd","text":"","code":"params <- list(n_dim = 1L, dim_size = 4L, order = 4L, p_rewire = 0.15) out <- nvd(sample_size = 1L, model = \"smallworld\", !!!params) #> ℹ Calling the `tidygraph::play_smallworld()` function with the following arguments: #> • n_dim: 1 #> • dim_size: 4 #> • order: 4 #> • p_rewire: 0.15 #> • loops: FALSE #> • multiple: FALSE as_nvd(out) #> [[1]] #> # A tbl_graph: 4 nodes and 6 edges #> # #> # An undirected simple graph with 1 component #> # #> # Node Data: 4 × 0 (active) #> # #> # Edge Data: 6 × 2 #> from to #> #> 1 1 2 #> 2 2 3 #> 3 3 4 #> # ℹ 3 more rows #> #> attr(,\"class\") #> [1] \"nvd\" \"list\""},{"path":"https://astamm.github.io/nevada/reference/as_vertex_partition.html","id":null,"dir":"Reference","previous_headings":"","what":"Coercion to Vertex Partition — as_vertex_partition","title":"Coercion to Vertex Partition — as_vertex_partition","text":"function converts vector memberships proper vertex partition object.","code":""},{"path":"https://astamm.github.io/nevada/reference/as_vertex_partition.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Coercion to Vertex Partition — as_vertex_partition","text":"","code":"as_vertex_partition(x)"},{"path":"https://astamm.github.io/nevada/reference/as_vertex_partition.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Coercion to Vertex Partition — as_vertex_partition","text":"x list grouping vertices partition element integer character vector vertex memberships.","code":""},{"path":"https://astamm.github.io/nevada/reference/as_vertex_partition.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Coercion to Vertex Partition — as_vertex_partition","text":"vertex_partition object storing corresponding vertex partition.","code":""},{"path":"https://astamm.github.io/nevada/reference/as_vertex_partition.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Coercion to Vertex Partition — as_vertex_partition","text":"","code":"m1 <- c(\"P1\", \"P3\", \"P4\", \"P1\", \"P2\", \"P2\", \"P3\", \"P1\", \"P4\", \"P3\") V1 <- as_vertex_partition(m1) m2 <- as.integer(c(1, 3, 4, 1, 2, 2, 3, 1, 4, 3)) V2 <- as_vertex_partition(m2)"},{"path":"https://astamm.github.io/nevada/reference/dist_nvd.html","id":null,"dir":"Reference","previous_headings":"","what":"Pairwise Distance Matrix Between Two Samples of Networks — dist_nvd","title":"Pairwise Distance Matrix Between Two Samples of Networks — dist_nvd","text":"function computes matrix pairwise distances elements two samples put together. cardinality fist sample denoted \\(n_1\\) second one denoted \\(n_2\\).","code":""},{"path":"https://astamm.github.io/nevada/reference/dist_nvd.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Pairwise Distance Matrix Between Two Samples of Networks — dist_nvd","text":"","code":"dist_nvd( x, y = NULL, representation = \"adjacency\", distance = \"frobenius\", matching_iterations = 0, target_matrix = NULL )"},{"path":"https://astamm.github.io/nevada/reference/dist_nvd.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Pairwise Distance Matrix Between Two Samples of Networks — dist_nvd","text":"x base::list tidygraph::tbl_graph objects matrix representations underlying networks given first population. y base::list tidygraph::tbl_graph objects matrix representations underlying networks given second population. representation string specifying desired type representation, among: \"adjacency\", \"laplacian\", \"modularity\" \"graphon\". Default \"laplacian\". distance string specifying chosen distance calculating test statistic, among: \"hamming\", \"frobenius\", \"spectral\" \"root-euclidean\". Default \"frobenius\". matching_iterations integer value specifying maximum number runs looking optimal permutation graph matching. Defaults 0L case matching done. target_matrix square numeric matrix size n equal order graphs specifying target matrix towards initial doubly stochastic matrix shrunk time graph matching algorithm fails provide good minimum. Defaults NULL case target matrix automatically chosen identity matrix uniform matrix n-simplex.","code":""},{"path":"https://astamm.github.io/nevada/reference/dist_nvd.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Pairwise Distance Matrix Between Two Samples of Networks — dist_nvd","text":"matrix dimension \\((n_1+n_2) \\times (n_1+n_2)\\) containing distances elements two samples put together.","code":""},{"path":"https://astamm.github.io/nevada/reference/dist_nvd.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Pairwise Distance Matrix Between Two Samples of Networks — dist_nvd","text":"","code":"gnp_params <- list(n = 24L, p = 1/3) degree_params <- list(out_degree = rep(2, 24L), method = \"configuration\") x <- nvd(sample_size = 10L, model = \"gnp\", !!!gnp_params) #> ℹ Calling the `tidygraph::play_gnp()` function with the following arguments: #> • n: 24 #> • p: 0.333333333333333 #> • directed: TRUE #> • loops: FALSE y <- nvd(sample_size = 10L, model = \"degree\", !!!degree_params) #> ℹ Calling the `tidygraph::play_degree()` function with the following arguments: #> • out_degree: 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, …, 2, and 2 #> • method: configuration #> • in_degree: NULL dist_nvd(x, y, \"adjacency\", \"spectral\") #> 1 2 3 4 5 6 7 #> 2 1.3247846 #> 3 1.0327248 0.9033180 #> 4 1.5853265 1.6640296 1.7191641 #> 5 0.9666449 1.4355136 1.2589486 1.3497579 #> 6 1.8110275 1.5013356 1.8511752 1.2436566 1.4344913 #> 7 1.3930286 1.4059886 1.5364497 1.1343736 1.0990257 0.9076238 #> 8 1.2303792 1.5106096 1.4119224 1.6730651 1.3688597 1.6864406 1.2009165 #> 9 1.1101856 1.2287318 1.3380202 1.5881906 0.9484409 1.3067718 0.9976968 #> 10 2.1893772 2.0652489 2.3058835 1.4329811 2.1422303 1.4517239 1.5917795 #> 11 8.4867947 8.5608153 8.7547574 7.4780207 8.2803750 7.4567586 7.7232314 #> 12 8.4422768 8.5215249 8.7216879 7.4711314 8.2429917 7.4256876 7.7030848 #> 13 8.3326960 8.4244411 8.6346130 7.2954696 8.0754004 7.2667769 7.5421763 #> 14 8.5346271 8.6472123 8.8305416 7.5621490 8.3493604 7.5456648 7.7836831 #> 15 8.4507363 8.5152352 8.7053939 7.4405549 8.2445197 7.4250752 7.6844996 #> 16 8.5612955 8.6429671 8.8154116 7.6008036 8.3980884 7.5923383 7.8293452 #> 17 8.7016700 8.7882495 8.9736385 7.7333608 8.5226313 7.6957167 7.9396531 #> 18 8.5984466 8.6848386 8.8748586 7.6466974 8.4189707 7.6032316 7.8775459 #> 19 8.5142376 8.6069190 8.7932205 7.5435473 8.3396354 7.5338812 7.7876685 #> 20 8.7145670 8.8895109 9.0224292 7.8085073 8.5666788 7.8687106 8.0494336 #> 8 9 10 11 12 13 14 #> 2 #> 3 #> 4 #> 5 #> 6 #> 7 #> 8 #> 9 1.1048100 #> 10 2.0321761 2.1846303 #> 11 8.3134499 8.4229044 6.6444501 #> 12 8.2746230 8.3994799 6.6304228 0.7369126 #> 13 8.1406785 8.2364872 6.5535510 1.2683823 1.3336147 #> 14 8.3549279 8.4946292 6.7359199 0.9783101 1.1464892 1.0788921 #> 15 8.2628771 8.3869980 6.6250181 0.7239710 0.6074279 1.3083881 1.1218164 #> 16 8.3952254 8.5488617 6.7202718 0.6934316 0.8810910 1.6705284 1.0485169 #> 17 8.5071303 8.6499853 6.8451125 1.1513150 1.5204346 1.6132610 1.0345899 #> 18 8.4544076 8.5696768 6.7655138 0.5638243 0.7853323 1.5476022 1.0788974 #> 19 8.3476217 8.4767803 6.6939736 0.5954485 0.6107754 1.4131486 0.9632040 #> 20 8.5461863 8.7305567 7.0410593 2.0052855 2.0542314 2.0288872 1.6862530 #> 15 16 17 18 19 #> 2 #> 3 #> 4 #> 5 #> 6 #> 7 #> 8 #> 9 #> 10 #> 11 #> 12 #> 13 #> 14 #> 15 #> 16 0.9222237 #> 17 1.5016252 1.1529340 #> 18 0.9899725 0.6758305 1.1875108 #> 19 0.5506270 0.7299532 1.3193354 0.6945410 #> 20 1.9859817 2.0844278 2.3432337 1.9666672 1.8500806"},{"path":"https://astamm.github.io/nevada/reference/distances.html","id":null,"dir":"Reference","previous_headings":"","what":"Distances Between Networks — distances","title":"Distances Between Networks — distances","text":"collection functions computing distance two networks.","code":""},{"path":"https://astamm.github.io/nevada/reference/distances.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Distances Between Networks — distances","text":"","code":"dist_hamming(x, y, representation = \"laplacian\") dist_frobenius( x, y, representation = \"laplacian\", matching_iterations = 0, target_matrix = NULL ) dist_spectral(x, y, representation = \"laplacian\") dist_root_euclidean(x, y, representation = \"laplacian\")"},{"path":"https://astamm.github.io/nevada/reference/distances.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Distances Between Networks — distances","text":"x tidygraph::tbl_graph object matrix representing underlying network. y tidygraph::tbl_graph object matrix representing underlying network. number vertices x. representation string specifying desired type representation, among: \"adjacency\", \"laplacian\", \"modularity\" \"graphon\". Default \"laplacian\". matching_iterations integer value specifying maximum number runs looking optimal permutation graph matching. Defaults 0L case matching done. target_matrix square numeric matrix size n equal order graphs specifying target matrix towards initial doubly stochastic matrix shrunk time graph matching algorithm fails provide good minimum. Defaults NULL case target matrix automatically chosen identity matrix uniform matrix n-simplex.","code":""},{"path":"https://astamm.github.io/nevada/reference/distances.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Distances Between Networks — distances","text":"scalar measuring distance two input networks.","code":""},{"path":"https://astamm.github.io/nevada/reference/distances.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Distances Between Networks — distances","text":"Let \\(X\\) matrix representation network \\(x\\) \\(Y\\) matrix representation network \\(y\\). Hamming distance \\(x\\) \\(y\\) given $$\\frac{1}{N(N-1)} \\sum_{,j} |X_{ij} - Y_{ij}|,$$ \\(N\\) number vertices networks \\(x\\) \\(y\\). Frobenius distance \\(x\\) \\(y\\) given $$\\sqrt{\\sum_{,j} (X_{ij} - Y_{ij})^2}.$$ spectral distance \\(x\\) \\(y\\) given $$\\sqrt{\\sum_i (a_i - b_i)^2},$$ \\(\\) \\(b\\) eigenvalues \\(X\\) \\(Y\\), respectively. distance gives rise classes equivalence. Consider spectral decomposition \\(X\\) \\(Y\\): $$X=VAV^{-1}$$ $$Y = UBU^{-1},$$ \\(V\\) \\(U\\) matrices whose columns eigenvectors \\(X\\) \\(Y\\), respectively \\(\\) \\(B\\) diagonal matrices elements eigenvalues \\(X\\) \\(Y\\), respectively. root-Euclidean distance \\(x\\) \\(y\\) given $$\\sqrt{\\sum_i (V \\sqrt{} V^{-1} - U \\sqrt{B} U^{-1})^2}.$$ Root-Euclidean distance can used laplacian matrix representation.","code":""},{"path":"https://astamm.github.io/nevada/reference/distances.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Distances Between Networks — distances","text":"","code":"g1 <- igraph::sample_gnp(20, 0.1) g2 <- igraph::sample_gnp(20, 0.2) dist_hamming(g1, g2, \"adjacency\") #> [1] 0.2526316 dist_frobenius(g1, g2, \"adjacency\") #> [1] 9.797959 dist_spectral(g1, g2, \"laplacian\") #> [1] 12.74562 dist_root_euclidean(g1, g2, \"laplacian\") #> [1] 10.22699"},{"path":"https://astamm.github.io/nevada/reference/edge_count_global_variables.html","id":null,"dir":"Reference","previous_headings":"","what":"Transform distance matrix in edge properties of minimal spanning tree — edge_count_global_variables","title":"Transform distance matrix in edge properties of minimal spanning tree — edge_count_global_variables","text":"Transform distance matrix edge properties minimal spanning tree","code":""},{"path":"https://astamm.github.io/nevada/reference/edge_count_global_variables.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Transform distance matrix in edge properties of minimal spanning tree — edge_count_global_variables","text":"","code":"edge_count_global_variables(d, n1, k = 1L)"},{"path":"https://astamm.github.io/nevada/reference/edge_count_global_variables.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Transform distance matrix in edge properties of minimal spanning tree — edge_count_global_variables","text":"d matrix dimension \\((n1+n2)x(n1+n2)\\) containing distances elements two samples put together. n1 integer giving size first sample. k integer specifying density minimal spanning tree generate.","code":""},{"path":"https://astamm.github.io/nevada/reference/edge_count_global_variables.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Transform distance matrix in edge properties of minimal spanning tree — edge_count_global_variables","text":"list edge properties minimal spanning tree.","code":""},{"path":"https://astamm.github.io/nevada/reference/edge_count_global_variables.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Transform distance matrix in edge properties of minimal spanning tree — edge_count_global_variables","text":"","code":"n1 <- 30L n2 <- 10L gnp_params <- list(n = 24L, p = 1/3) degree_params <- list(out_degree = rep(2, 24L), method = \"configuration\") x <- nvd(sample_size = n1, model = \"gnp\", !!!gnp_params) #> ℹ Calling the `tidygraph::play_gnp()` function with the following arguments: #> • n: 24 #> • p: 0.333333333333333 #> • directed: TRUE #> • loops: FALSE y <- nvd(sample_size = n2, model = \"degree\", !!!degree_params) #> ℹ Calling the `tidygraph::play_degree()` function with the following arguments: #> • out_degree: 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, …, 2, and 2 #> • method: configuration #> • in_degree: NULL d <- dist_nvd(x, y, representation = \"laplacian\", distance = \"frobenius\") e <- edge_count_global_variables(d, n1, k = 5L)"},{"path":"https://astamm.github.io/nevada/reference/generate_sigma_algebra.html","id":null,"dir":"Reference","previous_headings":"","what":"Sigma-Algebra generated by a Partition — generate_sigma_algebra","title":"Sigma-Algebra generated by a Partition — generate_sigma_algebra","text":"Sigma-Algebra generated Partition","code":""},{"path":"https://astamm.github.io/nevada/reference/generate_sigma_algebra.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Sigma-Algebra generated by a Partition — generate_sigma_algebra","text":"","code":"generate_sigma_algebra(x)"},{"path":"https://astamm.github.io/nevada/reference/generate_sigma_algebra.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Sigma-Algebra generated by a Partition — generate_sigma_algebra","text":"x Input partition stored vertex_partition object.","code":""},{"path":"https://astamm.github.io/nevada/reference/generate_sigma_algebra.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Sigma-Algebra generated by a Partition — generate_sigma_algebra","text":"Sigma-algebra","code":""},{"path":"https://astamm.github.io/nevada/reference/generate_sigma_algebra.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Sigma-Algebra generated by a Partition — generate_sigma_algebra","text":"","code":"g <- igraph::make_ring(7) m <- as.integer(c(1, 2, 1, 3, 4, 4, 3)) p <- as_vertex_partition(m) sa <- generate_sigma_algebra(p) all_full <- purrr::modify_depth(sa, 2, ~ subgraph_full (g, .x)) all_intra <- purrr::modify_depth(sa, 2, ~ subgraph_intra(g, .x)) all_inter <- purrr::modify_depth(sa, 2, ~ subgraph_inter(g, .x))"},{"path":"https://astamm.github.io/nevada/reference/inner-products.html","id":null,"dir":"Reference","previous_headings":"","what":"Inner-Products Between Networks — inner-products","title":"Inner-Products Between Networks — inner-products","text":"collection functions computing inner product two networks.","code":""},{"path":"https://astamm.github.io/nevada/reference/inner-products.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Inner-Products Between Networks — inner-products","text":"","code":"ipro_frobenius(x, y, representation = \"laplacian\")"},{"path":"https://astamm.github.io/nevada/reference/inner-products.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Inner-Products Between Networks — inner-products","text":"x igraph object matrix representing underlying network. y igraph object matrix representing underlying network. number vertices x. representation string specifying desired type representation, among: \"adjacency\", \"laplacian\", \"modularity\" \"graphon\". Default \"laplacian\".","code":""},{"path":"https://astamm.github.io/nevada/reference/inner-products.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Inner-Products Between Networks — inner-products","text":"scalar measuring angle two input networks.","code":""},{"path":"https://astamm.github.io/nevada/reference/inner-products.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Inner-Products Between Networks — inner-products","text":"","code":"g1 <- igraph::sample_gnp(20, 0.1) g2 <- igraph::sample_gnp(20, 0.2) ipro_frobenius(g1, g2, \"adjacency\") #> [1] 8"},{"path":"https://astamm.github.io/nevada/reference/mean.nvd.html","id":null,"dir":"Reference","previous_headings":"","what":"Fréchet Mean of Network-Valued Data — mean.nvd","title":"Fréchet Mean of Network-Valued Data — mean.nvd","text":"function computes sample Fréchet mean observed sample network-valued random variables according specified matrix representation. currently supports Euclidean geometry .e. sample Fréchet mean obtained argmin sum squared Frobenius distances.","code":""},{"path":"https://astamm.github.io/nevada/reference/mean.nvd.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Fréchet Mean of Network-Valued Data — mean.nvd","text":"","code":"# S3 method for class 'nvd' mean(x, weights = rep(1, length(x)), representation = \"adjacency\", ...)"},{"path":"https://astamm.github.io/nevada/reference/mean.nvd.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Fréchet Mean of Network-Valued Data — mean.nvd","text":"x nvd object. weights numeric vector specifying weights observation (default: equally weighted). representation string specifying graph representation used. Choices adjacency, laplacian, modularity, graphon. Default adjacency. ... argument parsed mean function.","code":""},{"path":"https://astamm.github.io/nevada/reference/mean.nvd.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Fréchet Mean of Network-Valued Data — mean.nvd","text":"mean network chosen matrix representation assuming Euclidean geometry now.","code":""},{"path":"https://astamm.github.io/nevada/reference/mean.nvd.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Fréchet Mean of Network-Valued Data — mean.nvd","text":"","code":"params <- list(n = 24L, p = 1/3) x <- nvd(sample_size = 1L, model = \"gnp\", !!!params) #> ℹ Calling the `tidygraph::play_gnp()` function with the following arguments: #> • n: 24 #> • p: 0.333333333333333 #> • directed: TRUE #> • loops: FALSE mean(x) #> [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12] [,13] #> [1,] 0 0 0 0 0 1 0 0 0 1 0 0 1 #> [2,] 1 0 0 1 1 0 1 1 0 0 1 0 1 #> [3,] 1 0 0 1 0 1 0 0 1 0 1 0 0 #> [4,] 0 1 0 0 0 0 1 0 1 1 0 1 0 #> [5,] 0 0 0 0 0 1 0 1 0 0 0 1 1 #> [6,] 0 0 0 0 1 0 1 0 1 0 0 0 0 #> [7,] 0 0 0 1 1 1 0 1 0 0 0 0 0 #> [8,] 1 0 1 0 0 0 1 0 0 0 0 0 0 #> [9,] 0 0 0 0 0 0 1 1 0 0 0 0 1 #> [10,] 1 0 0 0 0 1 1 1 0 0 0 1 0 #> [11,] 0 1 0 1 0 1 0 1 1 1 0 0 0 #> [12,] 0 0 1 1 0 1 1 1 0 0 1 0 1 #> [13,] 0 0 1 0 0 0 0 1 1 1 1 1 0 #> [14,] 1 0 0 0 1 0 0 0 1 1 1 0 1 #> [15,] 0 0 0 0 0 1 1 0 1 0 0 0 0 #> [16,] 0 0 0 0 0 0 0 0 0 0 0 0 0 #> [17,] 0 1 0 0 0 0 0 0 0 0 1 0 0 #> [18,] 0 0 0 1 0 1 1 1 1 1 0 1 0 #> [19,] 1 0 0 1 0 0 1 1 1 0 1 0 1 #> [20,] 0 1 0 0 0 0 0 0 0 0 0 1 0 #> [21,] 1 0 0 0 1 0 0 1 0 0 1 1 1 #> [22,] 0 0 0 0 1 1 0 0 0 1 1 1 0 #> [23,] 0 0 0 0 0 0 0 0 0 0 0 0 0 #> [24,] 0 0 0 1 0 1 1 0 0 0 0 0 0 #> [,14] [,15] [,16] [,17] [,18] [,19] [,20] [,21] [,22] [,23] [,24] #> [1,] 0 0 0 1 0 0 0 0 1 0 0 #> [2,] 0 0 0 0 1 0 1 1 1 1 1 #> [3,] 0 0 1 0 0 0 0 0 1 0 1 #> [4,] 1 0 0 1 0 0 0 1 0 0 0 #> [5,] 1 0 0 1 1 0 1 0 0 0 0 #> [6,] 1 0 0 1 0 0 0 0 0 1 0 #> [7,] 1 0 1 0 0 0 0 1 0 0 0 #> [8,] 0 0 0 0 1 1 1 0 1 1 0 #> [9,] 0 0 0 0 1 1 0 0 0 1 1 #> [10,] 0 1 1 0 0 1 0 0 1 1 0 #> [11,] 0 0 0 1 0 0 0 0 0 1 0 #> [12,] 1 1 0 0 1 0 1 0 0 1 1 #> [13,] 0 1 0 1 1 0 0 0 0 0 0 #> [14,] 0 0 0 0 0 1 0 0 1 0 0 #> [15,] 0 0 0 1 0 0 0 0 1 0 1 #> [16,] 0 0 0 0 0 0 1 0 0 0 1 #> [17,] 1 1 0 0 0 0 0 1 0 1 0 #> [18,] 0 1 0 0 0 0 0 1 1 0 0 #> [19,] 0 0 1 0 0 0 0 1 0 0 0 #> [20,] 0 0 0 0 1 1 0 0 1 1 1 #> [21,] 0 0 0 0 1 0 1 0 1 0 1 #> [22,] 1 1 0 0 0 0 0 0 0 0 1 #> [23,] 0 1 0 0 1 0 0 0 0 0 0 #> [24,] 0 1 0 0 0 1 0 0 0 0 0 #> attr(,\"representation\") #> [1] \"adjacency\""},{"path":"https://astamm.github.io/nevada/reference/nevada-package.html","id":null,"dir":"Reference","previous_headings":"","what":"nevada: Network-Valued Data Analysis — nevada-package","title":"nevada: Network-Valued Data Analysis — nevada-package","text":"flexible statistical framework network-valued data analysis. leverages complexity space distributions graphs using permutation framework inference implemented 'flipr' package. Currently, two-sample testing problem covered generalization k samples regression added future well. 4-step procedure user chooses suitable representation networks, suitable metric embed representation metric space, one test statistics target specific aspects distributions compared formula compute permutation p-value. Two types inference provided: global test answering whether difference distributions generated two samples local test localizing differences network structure. latter assumed shared networks samples. References: Lovato, ., Pini, ., Stamm, ., Vantini, S. (2020) \"Model-free two-sample test network-valued data\" doi:10.1016/j.csda.2019.106896 ; Lovato, ., Pini, ., Stamm, ., Taquet, M., Vantini, S. (2021) \"Multiscale null hypothesis testing network-valued data: Analysis brain networks patients autism\" doi:10.1111/rssc.12463 .","code":""},{"path":[]},{"path":"https://astamm.github.io/nevada/reference/nevada-package.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"nevada: Network-Valued Data Analysis — nevada-package","text":"Maintainer: Aymeric Stamm aymeric.stamm@cnrs.fr (ORCID) Authors: Ilenia Lovato ilenia.lovato01@universitadipavia.Alessia Pini alessia.pini@unicatt.Simone Vantini simone.vantini@polimi.","code":""},{"path":"https://astamm.github.io/nevada/reference/nvd-plot.html","id":null,"dir":"Reference","previous_headings":"","what":"MDS Visualization of Network Distributions — nvd-plot","title":"MDS Visualization of Network Distributions — nvd-plot","text":"function generates 2-dimensional plots samples networks via multi-dimensional scaling using representations distances included package.","code":""},{"path":"https://astamm.github.io/nevada/reference/nvd-plot.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"MDS Visualization of Network Distributions — nvd-plot","text":"","code":"# S3 method for class 'nvd' autoplot(object, memberships = rep(1, length(object)), method = \"mds\", ...) # S3 method for class 'nvd' plot(x, method = \"mds\", ...)"},{"path":"https://astamm.github.io/nevada/reference/nvd-plot.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"MDS Visualization of Network Distributions — nvd-plot","text":"object, x list containing two samples network-valued data stored objects class nvd. memberships integer vector specifying membership network specific sample. Defaults rep(1, length(nvd)) assumes networks input nvd object belong single group. method string specifying dimensionality reduction method use projecting samples cartesian plane. Choices \"mds\", \"tsne\" \"umap\". Defaults \"mds\". ... Extra arguments passed plot function.","code":""},{"path":"https://astamm.github.io/nevada/reference/nvd-plot.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"MDS Visualization of Network Distributions — nvd-plot","text":"Invisibly returns ggplot object. particular, data set computed generate plot can retrieved via $data. tibble containing following variables: V1: x-coordinate observation plane, V2: y-coordinate observation plane, Label: sample membership observation, Representation: type matrix representation used manipulate observation, Distance: distance used measure far observation others.","code":""},{"path":"https://astamm.github.io/nevada/reference/nvd-plot.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"MDS Visualization of Network Distributions — nvd-plot","text":"","code":"gnp_params <- list(n = 24L, p = 1/3) degree_params <- list(out_degree = rep(2, 24L), method = \"configuration\") x <- nvd(sample_size = 10L, model = \"gnp\", !!!gnp_params) #> ℹ Calling the `tidygraph::play_gnp()` function with the following arguments: #> • n: 24 #> • p: 0.333333333333333 #> • directed: TRUE #> • loops: FALSE y <- nvd(sample_size = 10L, model = \"degree\", !!!degree_params) #> ℹ Calling the `tidygraph::play_degree()` function with the following arguments: #> • out_degree: 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, …, 2, and 2 #> • method: configuration #> • in_degree: NULL mb <- c(rep(1, length(x)), rep(2, length(y))) z <- as_nvd(c(x, y)) ggplot2::autoplot(z, memberships = mb) plot(z, memberships = mb)"},{"path":"https://astamm.github.io/nevada/reference/nvd.html","id":null,"dir":"Reference","previous_headings":"","what":"Network-Valued Data Constructor — nvd","title":"Network-Valued Data Constructor — nvd","text":"constructor objects class nvd.","code":""},{"path":"https://astamm.github.io/nevada/reference/nvd.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Network-Valued Data Constructor — nvd","text":"","code":"nvd(sample_size, model, ...)"},{"path":"https://astamm.github.io/nevada/reference/nvd.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Network-Valued Data Constructor — nvd","text":"sample_size integer specifying sample size. model string specifying model used sampling networks. tidygraph::play_ functions supported. model name corresponds name function without play_ prefix. ... Model parameters passed model function.","code":""},{"path":"https://astamm.github.io/nevada/reference/nvd.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Network-Valued Data Constructor — nvd","text":"nvd object list tidygraph::tbl_graph objects.","code":""},{"path":"https://astamm.github.io/nevada/reference/nvd.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Network-Valued Data Constructor — nvd","text":"","code":"params <- list(n_dim = 1L, dim_size = 4L, order = 4L, p_rewire = 0.15) nvd(sample_size = 1L, model = \"smallworld\", !!!params) #> ℹ Calling the `tidygraph::play_smallworld()` function with the following arguments: #> • n_dim: 1 #> • dim_size: 4 #> • order: 4 #> • p_rewire: 0.15 #> • loops: FALSE #> • multiple: FALSE #> [[1]] #> # A tbl_graph: 4 nodes and 6 edges #> # #> # An undirected simple graph with 1 component #> # #> # Node Data: 4 × 0 (active) #> # #> # Edge Data: 6 × 2 #> from to #> #> 1 1 2 #> 2 2 3 #> 3 3 4 #> # ℹ 3 more rows #> #> attr(,\"class\") #> [1] \"nvd\" \"list\""},{"path":"https://astamm.github.io/nevada/reference/pipe.html","id":null,"dir":"Reference","previous_headings":"","what":"Pipe operator — %>%","title":"Pipe operator — %>%","text":"See magrittr::%>% details.","code":""},{"path":"https://astamm.github.io/nevada/reference/pipe.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Pipe operator — %>%","text":"","code":"lhs %>% rhs"},{"path":"https://astamm.github.io/nevada/reference/pipe.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Pipe operator — %>%","text":"lhs value magrittr placeholder. rhs function call using magrittr semantics.","code":""},{"path":"https://astamm.github.io/nevada/reference/pipe.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Pipe operator — %>%","text":"result calling rhs(lhs).","code":""},{"path":"https://astamm.github.io/nevada/reference/power2.html","id":null,"dir":"Reference","previous_headings":"","what":"Power Simulations for Permutation Tests — power2","title":"Power Simulations for Permutation Tests — power2","text":"function provides Monte-Carlo estimate power permutation tests proposed package.","code":""},{"path":"https://astamm.github.io/nevada/reference/power2.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Power Simulations for Permutation Tests — power2","text":"","code":"power2( sample_size1, model1, params1, sample_size2, model2, params2, representation = \"adjacency\", distance = \"frobenius\", stats = c(\"flipr:t_ip\", \"flipr:f_ip\"), B = 1000L, alpha = 0.05, test = \"exact\", k = 5L, R = 1000L )"},{"path":"https://astamm.github.io/nevada/reference/power2.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Power Simulations for Permutation Tests — power2","text":"sample_size1 integer specifying size first sample. model1 string specifying model used sampling networks first sample. tidygraph::play_ functions supported. model name corresponds name function without play_ prefix. params1 list specifying parameters passed model function generate first sample. sample_size2 integer specifying size second sample. model2 string specifying model used sampling networks second sample. tidygraph::play_ functions supported. model name corresponds name function without play_ prefix. params2 list specifying parameters passed model representation string specifying desired type representation, among: \"adjacency\", \"laplacian\" \"modularity\". Defaults \"adjacency\". distance string specifying chosen distance calculating test statistic, among: \"hamming\", \"frobenius\", \"spectral\" \"root-euclidean\". Defaults \"frobenius\". stats character vector specifying chosen test statistic(s), among: \"original_edge_count\", \"generalized_edge_count\", \"weighted_edge_count\", \"student_euclidean\", \"welch_euclidean\" statistics based inter-point distances available flipr package: \"flipr:student_ip\", \"flipr:fisher_ip\", \"flipr:bg_ip\", \"flipr:energy_ip\", \"flipr:cq_ip\". Defaults c(\"flipr:student_ip\", \"flipr:fisher_ip\"). B number permutation tolerance. number lower 1, intended tolerance. Otherwise, intended number required permutations. Defaults 1000L. alpha Significance level hypothesis testing. Defaults 0.05. test character string specifying formula used compute permutation p-value. Choices \"estimate\", \"upper_bound\" \"exact\". Defaults \"exact\" provides exact tests. k integer specifying density minimum spanning tree used edge count statistics. Defaults 5L. R Number Monte-Carlo trials used estimate power. Defaults 1000L.","code":""},{"path":"https://astamm.github.io/nevada/reference/power2.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Power Simulations for Permutation Tests — power2","text":"numeric value estimating power test.","code":""},{"path":"https://astamm.github.io/nevada/reference/power2.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Power Simulations for Permutation Tests — power2","text":"Currently, six scenarios pairs populations implemented. Scenario 0 allows make sure permutation tests exact.","code":""},{"path":"https://astamm.github.io/nevada/reference/power2.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Power Simulations for Permutation Tests — power2","text":"","code":"gnp_params <- list(n = 24L, p = 1/3) degree_params <- list(out_degree = rep(2, 24L), method = \"configuration\") power2( sample_size1 = 10L, model1 = \"gnp\", params1 = gnp_params, sample_size2 = 10L, model2 = \"degree\", params2 = degree_params, R = 10L, B = 100L ) #> ℹ Calling the `tidygraph::play_gnp()` function with the following arguments: #> • n: 24 #> • p: 0.333333333333333 #> • directed: TRUE #> • loops: FALSE #> ℹ Calling the `tidygraph::play_degree()` function with the following arguments: #> • out_degree: 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, …, 2, and 2 #> • method: configuration #> • in_degree: NULL #> ! Setting the seed for sampling permutations is mandatory for obtaining a continuous p-value function. Using `seed = 1234`. #> ℹ Calling the `tidygraph::play_gnp()` function with the following arguments: #> • n: 24 #> • p: 0.333333333333333 #> • directed: TRUE #> • loops: FALSE #> ℹ Calling the `tidygraph::play_degree()` function with the following arguments: #> • out_degree: 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, …, 2, and 2 #> • method: configuration #> • in_degree: NULL #> ! Setting the seed for sampling permutations is mandatory for obtaining a continuous p-value function. Using `seed = 1234`. #> ℹ Calling the `tidygraph::play_gnp()` function with the following arguments: #> • n: 24 #> • p: 0.333333333333333 #> • directed: TRUE #> • loops: FALSE #> ℹ Calling the `tidygraph::play_degree()` function with the following arguments: #> • out_degree: 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, …, 2, and 2 #> • method: configuration #> • in_degree: NULL #> ! Setting the seed for sampling permutations is mandatory for obtaining a continuous p-value function. Using `seed = 1234`. #> ℹ Calling the `tidygraph::play_gnp()` function with the following arguments: #> • n: 24 #> • p: 0.333333333333333 #> • directed: TRUE #> • loops: FALSE #> ℹ Calling the `tidygraph::play_degree()` function with the following arguments: #> • out_degree: 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, …, 2, and 2 #> • method: configuration #> • in_degree: NULL #> ! Setting the seed for sampling permutations is mandatory for obtaining a continuous p-value function. Using `seed = 1234`. #> ℹ Calling the `tidygraph::play_gnp()` function with the following arguments: #> • n: 24 #> • p: 0.333333333333333 #> • directed: TRUE #> • loops: FALSE #> ℹ Calling the `tidygraph::play_degree()` function with the following arguments: #> • out_degree: 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, …, 2, and 2 #> • method: configuration #> • in_degree: NULL #> ! Setting the seed for sampling permutations is mandatory for obtaining a continuous p-value function. Using `seed = 1234`. #> ℹ Calling the `tidygraph::play_gnp()` function with the following arguments: #> • n: 24 #> • p: 0.333333333333333 #> • directed: TRUE #> • loops: FALSE #> ℹ Calling the `tidygraph::play_degree()` function with the following arguments: #> • out_degree: 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, …, 2, and 2 #> • method: configuration #> • in_degree: NULL #> ! Setting the seed for sampling permutations is mandatory for obtaining a continuous p-value function. Using `seed = 1234`. #> ℹ Calling the `tidygraph::play_gnp()` function with the following arguments: #> • n: 24 #> • p: 0.333333333333333 #> • directed: TRUE #> • loops: FALSE #> ℹ Calling the `tidygraph::play_degree()` function with the following arguments: #> • out_degree: 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, …, 2, and 2 #> • method: configuration #> • in_degree: NULL #> ! Setting the seed for sampling permutations is mandatory for obtaining a continuous p-value function. Using `seed = 1234`. #> ℹ Calling the `tidygraph::play_gnp()` function with the following arguments: #> • n: 24 #> • p: 0.333333333333333 #> • directed: TRUE #> • loops: FALSE #> ℹ Calling the `tidygraph::play_degree()` function with the following arguments: #> • out_degree: 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, …, 2, and 2 #> • method: configuration #> • in_degree: NULL #> ! Setting the seed for sampling permutations is mandatory for obtaining a continuous p-value function. Using `seed = 1234`. #> ℹ Calling the `tidygraph::play_gnp()` function with the following arguments: #> • n: 24 #> • p: 0.333333333333333 #> • directed: TRUE #> • loops: FALSE #> ℹ Calling the `tidygraph::play_degree()` function with the following arguments: #> • out_degree: 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, …, 2, and 2 #> • method: configuration #> • in_degree: NULL #> ! Setting the seed for sampling permutations is mandatory for obtaining a continuous p-value function. Using `seed = 1234`. #> ℹ Calling the `tidygraph::play_gnp()` function with the following arguments: #> • n: 24 #> • p: 0.333333333333333 #> • directed: TRUE #> • loops: FALSE #> ℹ Calling the `tidygraph::play_degree()` function with the following arguments: #> • out_degree: 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, …, 2, and 2 #> • method: configuration #> • in_degree: NULL #> ! Setting the seed for sampling permutations is mandatory for obtaining a continuous p-value function. Using `seed = 1234`. #> [1] 1"},{"path":"https://astamm.github.io/nevada/reference/push_to_graph_space.html","id":null,"dir":"Reference","previous_headings":"","what":"Graph Sample Embeddings — push_to_graph_space","title":"Graph Sample Embeddings — push_to_graph_space","text":"collection functions embed sample graphs suitable spaces statistical analysis.","code":""},{"path":"https://astamm.github.io/nevada/reference/push_to_graph_space.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Graph Sample Embeddings — push_to_graph_space","text":"","code":"push_to_graph_space(obj)"},{"path":"https://astamm.github.io/nevada/reference/push_to_graph_space.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Graph Sample Embeddings — push_to_graph_space","text":"obj object class nvd containing sample graphs.","code":""},{"path":"https://astamm.github.io/nevada/reference/push_to_graph_space.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Graph Sample Embeddings — push_to_graph_space","text":"object class nvd containing sample graphs graph space.","code":""},{"path":"https://astamm.github.io/nevada/reference/push_to_graph_space.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Graph Sample Embeddings — push_to_graph_space","text":"","code":"x <- nvd(sample_size = 5L, model = \"gnp\", n = 24L, p = 1/3) #> ℹ Calling the `tidygraph::play_gnp()` function with the following arguments: #> • n: 24 #> • p: 0.333333333333333 #> • directed: TRUE #> • loops: FALSE x <- push_to_graph_space(x) #> ℹ Graphs have the following number of vertices: 24, 24, 24, 24, and 24"},{"path":"https://astamm.github.io/nevada/reference/repr_nvd.html","id":null,"dir":"Reference","previous_headings":"","what":"Network-Valued to Matrix-Valued Data — repr_nvd","title":"Network-Valued to Matrix-Valued Data — repr_nvd","text":"Network-Valued Matrix-Valued Data","code":""},{"path":"https://astamm.github.io/nevada/reference/repr_nvd.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Network-Valued to Matrix-Valued Data — repr_nvd","text":"","code":"repr_nvd(x, y = NULL, representation = \"adjacency\")"},{"path":"https://astamm.github.io/nevada/reference/repr_nvd.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Network-Valued to Matrix-Valued Data — repr_nvd","text":"x nvd object. y nvd object. NULL (default), taken account. representation string specifying requested matrix representation. Choices : \"adjacency\", \"laplacian\" \"modularity\". Default \"adjacency\".","code":""},{"path":"https://astamm.github.io/nevada/reference/repr_nvd.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Network-Valued to Matrix-Valued Data — repr_nvd","text":"list matrices.","code":""},{"path":"https://astamm.github.io/nevada/reference/repr_nvd.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Network-Valued to Matrix-Valued Data — repr_nvd","text":"","code":"params <- list(n = 24L, p = 1/3) x <- nvd(sample_size = 1L, model = \"gnp\", !!!params) #> ℹ Calling the `tidygraph::play_gnp()` function with the following arguments: #> • n: 24 #> • p: 0.333333333333333 #> • directed: TRUE #> • loops: FALSE xm <- repr_nvd(x)"},{"path":"https://astamm.github.io/nevada/reference/representations.html","id":null,"dir":"Reference","previous_headings":"","what":"Network Representation Functions — representations","title":"Network Representation Functions — representations","text":"collection functions convert graph stored igraph object desired matrix representation among adjacency matrix, graph laplacian, modularity matrix graphon (edge probability matrix).","code":""},{"path":"https://astamm.github.io/nevada/reference/representations.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Network Representation Functions — representations","text":"","code":"repr_adjacency(network, validate = TRUE) repr_laplacian(network, validate = TRUE) repr_modularity(network, validate = TRUE) repr_graphon(network, validate = TRUE)"},{"path":"https://astamm.github.io/nevada/reference/representations.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Network Representation Functions — representations","text":"network igraph object. validate boolean specifying whether function check class input (default: TRUE).","code":""},{"path":"https://astamm.github.io/nevada/reference/representations.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Network Representation Functions — representations","text":"numeric square matrix giving desired network representation recorded object's class.","code":""},{"path":"https://astamm.github.io/nevada/reference/representations.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Network Representation Functions — representations","text":"","code":"g <- igraph::sample_smallworld(1, 25, 3, 0.05) repr_adjacency(g) #> [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12] [,13] #> [1,] 0 1 1 1 0 0 0 0 0 0 0 0 0 #> [2,] 1 0 1 1 1 0 0 0 0 0 0 0 0 #> [3,] 1 1 0 1 1 1 0 0 0 0 0 0 0 #> [4,] 1 1 1 0 1 1 1 0 0 0 0 0 0 #> [5,] 0 1 1 1 0 1 1 1 0 0 0 0 0 #> [6,] 0 0 1 1 1 0 1 1 1 0 0 0 0 #> [7,] 0 0 0 1 1 1 0 1 1 1 0 0 0 #> [8,] 0 0 0 0 1 1 1 0 1 1 1 0 0 #> [9,] 0 0 0 0 0 1 1 1 0 1 1 1 0 #> [10,] 0 0 0 0 0 0 1 1 1 0 1 1 1 #> [11,] 0 0 0 0 0 0 0 1 1 1 0 1 1 #> [12,] 0 0 0 0 0 0 0 0 1 1 1 0 1 #> [13,] 0 0 0 0 0 0 0 0 0 1 1 1 0 #> [14,] 0 0 0 0 0 0 0 0 0 0 0 1 1 #> [15,] 0 0 0 0 0 0 0 0 0 0 0 1 1 #> [16,] 0 0 0 0 0 0 0 0 0 0 0 0 1 #> [17,] 0 0 0 0 0 0 0 0 0 0 1 0 0 #> [18,] 0 0 0 0 0 0 0 0 0 0 0 0 0 #> [19,] 0 0 0 0 0 0 0 0 0 0 0 0 0 #> [20,] 0 0 0 0 0 0 0 0 0 0 0 0 0 #> [21,] 0 0 0 0 0 0 0 0 0 0 0 0 0 #> [22,] 0 0 0 0 0 0 0 0 0 0 0 0 0 #> [23,] 1 0 0 0 0 0 0 0 0 0 0 0 0 #> [24,] 1 1 0 0 0 0 0 0 0 0 0 0 0 #> [25,] 1 1 0 0 0 0 0 0 0 0 1 0 0 #> [,14] [,15] [,16] [,17] [,18] [,19] [,20] [,21] [,22] [,23] [,24] [,25] #> [1,] 0 0 0 0 0 0 0 0 0 1 1 1 #> [2,] 0 0 0 0 0 0 0 0 0 0 1 1 #> [3,] 0 0 0 0 0 0 0 0 0 0 0 0 #> [4,] 0 0 0 0 0 0 0 0 0 0 0 0 #> [5,] 0 0 0 0 0 0 0 0 0 0 0 0 #> [6,] 0 0 0 0 0 0 0 0 0 0 0 0 #> [7,] 0 0 0 0 0 0 0 0 0 0 0 0 #> [8,] 0 0 0 0 0 0 0 0 0 0 0 0 #> [9,] 0 0 0 0 0 0 0 0 0 0 0 0 #> [10,] 0 0 0 0 0 0 0 0 0 0 0 0 #> [11,] 0 0 0 1 0 0 0 0 0 0 0 1 #> [12,] 1 1 0 0 0 0 0 0 0 0 0 0 #> [13,] 1 1 1 0 0 0 0 0 0 0 0 0 #> [14,] 0 1 1 1 0 0 0 0 0 0 0 0 #> [15,] 1 0 1 1 0 0 0 0 0 1 0 0 #> [16,] 1 1 0 1 1 1 0 0 0 0 0 0 #> [17,] 1 1 1 0 1 1 1 1 0 0 0 0 #> [18,] 0 0 1 1 0 1 1 1 0 0 0 0 #> [19,] 0 0 1 1 1 0 1 1 1 0 0 0 #> [20,] 0 0 0 1 1 1 0 0 1 1 0 0 #> [21,] 0 0 0 1 1 1 0 0 1 1 1 0 #> [22,] 0 0 0 0 0 1 1 1 0 1 1 1 #> [23,] 0 1 0 0 0 0 1 1 1 0 1 1 #> [24,] 0 0 0 0 0 0 0 1 1 1 0 1 #> [25,] 0 0 0 0 0 0 0 0 1 1 1 0 #> attr(,\"representation\") #> [1] \"adjacency\" repr_laplacian(g) #> [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12] [,13] #> [1,] 6 -1 -1 -1 0 0 0 0 0 0 0 0 0 #> [2,] -1 6 -1 -1 -1 0 0 0 0 0 0 0 0 #> [3,] -1 -1 5 -1 -1 -1 0 0 0 0 0 0 0 #> [4,] -1 -1 -1 6 -1 -1 -1 0 0 0 0 0 0 #> [5,] 0 -1 -1 -1 6 -1 -1 -1 0 0 0 0 0 #> [6,] 0 0 -1 -1 -1 6 -1 -1 -1 0 0 0 0 #> [7,] 0 0 0 -1 -1 -1 6 -1 -1 -1 0 0 0 #> [8,] 0 0 0 0 -1 -1 -1 6 -1 -1 -1 0 0 #> [9,] 0 0 0 0 0 -1 -1 -1 6 -1 -1 -1 0 #> [10,] 0 0 0 0 0 0 -1 -1 -1 6 -1 -1 -1 #> [11,] 0 0 0 0 0 0 0 -1 -1 -1 7 -1 -1 #> [12,] 0 0 0 0 0 0 0 0 -1 -1 -1 6 -1 #> [13,] 0 0 0 0 0 0 0 0 0 -1 -1 -1 6 #> [14,] 0 0 0 0 0 0 0 0 0 0 0 -1 -1 #> [15,] 0 0 0 0 0 0 0 0 0 0 0 -1 -1 #> [16,] 0 0 0 0 0 0 0 0 0 0 0 0 -1 #> [17,] 0 0 0 0 0 0 0 0 0 0 -1 0 0 #> [18,] 0 0 0 0 0 0 0 0 0 0 0 0 0 #> [19,] 0 0 0 0 0 0 0 0 0 0 0 0 0 #> [20,] 0 0 0 0 0 0 0 0 0 0 0 0 0 #> [21,] 0 0 0 0 0 0 0 0 0 0 0 0 0 #> [22,] 0 0 0 0 0 0 0 0 0 0 0 0 0 #> [23,] -1 0 0 0 0 0 0 0 0 0 0 0 0 #> [24,] -1 -1 0 0 0 0 0 0 0 0 0 0 0 #> [25,] -1 -1 0 0 0 0 0 0 0 0 -1 0 0 #> [,14] [,15] [,16] [,17] [,18] [,19] [,20] [,21] [,22] [,23] [,24] [,25] #> [1,] 0 0 0 0 0 0 0 0 0 -1 -1 -1 #> [2,] 0 0 0 0 0 0 0 0 0 0 -1 -1 #> [3,] 0 0 0 0 0 0 0 0 0 0 0 0 #> [4,] 0 0 0 0 0 0 0 0 0 0 0 0 #> [5,] 0 0 0 0 0 0 0 0 0 0 0 0 #> [6,] 0 0 0 0 0 0 0 0 0 0 0 0 #> [7,] 0 0 0 0 0 0 0 0 0 0 0 0 #> [8,] 0 0 0 0 0 0 0 0 0 0 0 0 #> [9,] 0 0 0 0 0 0 0 0 0 0 0 0 #> [10,] 0 0 0 0 0 0 0 0 0 0 0 0 #> [11,] 0 0 0 -1 0 0 0 0 0 0 0 -1 #> [12,] -1 -1 0 0 0 0 0 0 0 0 0 0 #> [13,] -1 -1 -1 0 0 0 0 0 0 0 0 0 #> [14,] 5 -1 -1 -1 0 0 0 0 0 0 0 0 #> [15,] -1 6 -1 -1 0 0 0 0 0 -1 0 0 #> [16,] -1 -1 6 -1 -1 -1 0 0 0 0 0 0 #> [17,] -1 -1 -1 8 -1 -1 -1 -1 0 0 0 0 #> [18,] 0 0 -1 -1 5 -1 -1 -1 0 0 0 0 #> [19,] 0 0 -1 -1 -1 6 -1 -1 -1 0 0 0 #> [20,] 0 0 0 -1 -1 -1 5 0 -1 -1 0 0 #> [21,] 0 0 0 -1 -1 -1 0 6 -1 -1 -1 0 #> [22,] 0 0 0 0 0 -1 -1 -1 6 -1 -1 -1 #> [23,] 0 -1 0 0 0 0 -1 -1 -1 7 -1 -1 #> [24,] 0 0 0 0 0 0 0 -1 -1 -1 6 -1 #> [25,] 0 0 0 0 0 0 0 0 -1 -1 -1 6 #> attr(,\"representation\") #> [1] \"laplacian\" repr_modularity(g) #> [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] #> [1,] -0.24 0.76 0.8000000 0.76 -0.24 -0.24 -0.24 -0.24 -0.24 -0.24 #> [2,] 0.76 -0.24 0.8000000 0.76 0.76 -0.24 -0.24 -0.24 -0.24 -0.24 #> [3,] 0.80 0.80 -0.1666667 0.80 0.80 0.80 -0.20 -0.20 -0.20 -0.20 #> [4,] 0.76 0.76 0.8000000 -0.24 0.76 0.76 0.76 -0.24 -0.24 -0.24 #> [5,] -0.24 0.76 0.8000000 0.76 -0.24 0.76 0.76 0.76 -0.24 -0.24 #> [6,] -0.24 -0.24 0.8000000 0.76 0.76 -0.24 0.76 0.76 0.76 -0.24 #> [7,] -0.24 -0.24 -0.2000000 0.76 0.76 0.76 -0.24 0.76 0.76 0.76 #> [8,] -0.24 -0.24 -0.2000000 -0.24 0.76 0.76 0.76 -0.24 0.76 0.76 #> [9,] -0.24 -0.24 -0.2000000 -0.24 -0.24 0.76 0.76 0.76 -0.24 0.76 #> [10,] -0.24 -0.24 -0.2000000 -0.24 -0.24 -0.24 0.76 0.76 0.76 -0.24 #> [11,] -0.28 -0.28 -0.2333333 -0.28 -0.28 -0.28 -0.28 0.72 0.72 0.72 #> [12,] -0.24 -0.24 -0.2000000 -0.24 -0.24 -0.24 -0.24 -0.24 0.76 0.76 #> [13,] -0.24 -0.24 -0.2000000 -0.24 -0.24 -0.24 -0.24 -0.24 -0.24 0.76 #> [14,] -0.20 -0.20 -0.1666667 -0.20 -0.20 -0.20 -0.20 -0.20 -0.20 -0.20 #> [15,] -0.24 -0.24 -0.2000000 -0.24 -0.24 -0.24 -0.24 -0.24 -0.24 -0.24 #> [16,] -0.24 -0.24 -0.2000000 -0.24 -0.24 -0.24 -0.24 -0.24 -0.24 -0.24 #> [17,] -0.32 -0.32 -0.2666667 -0.32 -0.32 -0.32 -0.32 -0.32 -0.32 -0.32 #> [18,] -0.20 -0.20 -0.1666667 -0.20 -0.20 -0.20 -0.20 -0.20 -0.20 -0.20 #> [19,] -0.24 -0.24 -0.2000000 -0.24 -0.24 -0.24 -0.24 -0.24 -0.24 -0.24 #> [20,] -0.20 -0.20 -0.1666667 -0.20 -0.20 -0.20 -0.20 -0.20 -0.20 -0.20 #> [21,] -0.24 -0.24 -0.2000000 -0.24 -0.24 -0.24 -0.24 -0.24 -0.24 -0.24 #> [22,] -0.24 -0.24 -0.2000000 -0.24 -0.24 -0.24 -0.24 -0.24 -0.24 -0.24 #> [23,] 0.72 -0.28 -0.2333333 -0.28 -0.28 -0.28 -0.28 -0.28 -0.28 -0.28 #> [24,] 0.76 0.76 -0.2000000 -0.24 -0.24 -0.24 -0.24 -0.24 -0.24 -0.24 #> [25,] 0.76 0.76 -0.2000000 -0.24 -0.24 -0.24 -0.24 -0.24 -0.24 -0.24 #> [,11] [,12] [,13] [,14] [,15] [,16] [,17] [,18] [,19] #> [1,] -0.2800000 -0.24 -0.24 -0.2000000 -0.24 -0.24 -0.3200000 -0.2000000 -0.24 #> [2,] -0.2800000 -0.24 -0.24 -0.2000000 -0.24 -0.24 -0.3200000 -0.2000000 -0.24 #> [3,] -0.2333333 -0.20 -0.20 -0.1666667 -0.20 -0.20 -0.2666667 -0.1666667 -0.20 #> [4,] -0.2800000 -0.24 -0.24 -0.2000000 -0.24 -0.24 -0.3200000 -0.2000000 -0.24 #> [5,] -0.2800000 -0.24 -0.24 -0.2000000 -0.24 -0.24 -0.3200000 -0.2000000 -0.24 #> [6,] -0.2800000 -0.24 -0.24 -0.2000000 -0.24 -0.24 -0.3200000 -0.2000000 -0.24 #> [7,] -0.2800000 -0.24 -0.24 -0.2000000 -0.24 -0.24 -0.3200000 -0.2000000 -0.24 #> [8,] 0.7200000 -0.24 -0.24 -0.2000000 -0.24 -0.24 -0.3200000 -0.2000000 -0.24 #> [9,] 0.7200000 0.76 -0.24 -0.2000000 -0.24 -0.24 -0.3200000 -0.2000000 -0.24 #> [10,] 0.7200000 0.76 0.76 -0.2000000 -0.24 -0.24 -0.3200000 -0.2000000 -0.24 #> [11,] -0.3266667 0.72 0.72 -0.2333333 -0.28 -0.28 0.6266667 -0.2333333 -0.28 #> [12,] 0.7200000 -0.24 0.76 0.8000000 0.76 -0.24 -0.3200000 -0.2000000 -0.24 #> [13,] 0.7200000 0.76 -0.24 0.8000000 0.76 0.76 -0.3200000 -0.2000000 -0.24 #> [14,] -0.2333333 0.80 0.80 -0.1666667 0.80 0.80 0.7333333 -0.1666667 -0.20 #> [15,] -0.2800000 0.76 0.76 0.8000000 -0.24 0.76 0.6800000 -0.2000000 -0.24 #> [16,] -0.2800000 -0.24 0.76 0.8000000 0.76 -0.24 0.6800000 0.8000000 0.76 #> [17,] 0.6266667 -0.32 -0.32 0.7333333 0.68 0.68 -0.4266667 0.7333333 0.68 #> [18,] -0.2333333 -0.20 -0.20 -0.1666667 -0.20 0.80 0.7333333 -0.1666667 0.80 #> [19,] -0.2800000 -0.24 -0.24 -0.2000000 -0.24 0.76 0.6800000 0.8000000 -0.24 #> [20,] -0.2333333 -0.20 -0.20 -0.1666667 -0.20 -0.20 0.7333333 0.8333333 0.80 #> [21,] -0.2800000 -0.24 -0.24 -0.2000000 -0.24 -0.24 0.6800000 0.8000000 0.76 #> [22,] -0.2800000 -0.24 -0.24 -0.2000000 -0.24 -0.24 -0.3200000 -0.2000000 0.76 #> [23,] -0.3266667 -0.28 -0.28 -0.2333333 0.72 -0.28 -0.3733333 -0.2333333 -0.28 #> [24,] -0.2800000 -0.24 -0.24 -0.2000000 -0.24 -0.24 -0.3200000 -0.2000000 -0.24 #> [25,] 0.7200000 -0.24 -0.24 -0.2000000 -0.24 -0.24 -0.3200000 -0.2000000 -0.24 #> [,20] [,21] [,22] [,23] [,24] [,25] #> [1,] -0.2000000 -0.24 -0.24 0.7200000 0.76 0.76 #> [2,] -0.2000000 -0.24 -0.24 -0.2800000 0.76 0.76 #> [3,] -0.1666667 -0.20 -0.20 -0.2333333 -0.20 -0.20 #> [4,] -0.2000000 -0.24 -0.24 -0.2800000 -0.24 -0.24 #> [5,] -0.2000000 -0.24 -0.24 -0.2800000 -0.24 -0.24 #> [6,] -0.2000000 -0.24 -0.24 -0.2800000 -0.24 -0.24 #> [7,] -0.2000000 -0.24 -0.24 -0.2800000 -0.24 -0.24 #> [8,] -0.2000000 -0.24 -0.24 -0.2800000 -0.24 -0.24 #> [9,] -0.2000000 -0.24 -0.24 -0.2800000 -0.24 -0.24 #> [10,] -0.2000000 -0.24 -0.24 -0.2800000 -0.24 -0.24 #> [11,] -0.2333333 -0.28 -0.28 -0.3266667 -0.28 0.72 #> [12,] -0.2000000 -0.24 -0.24 -0.2800000 -0.24 -0.24 #> [13,] -0.2000000 -0.24 -0.24 -0.2800000 -0.24 -0.24 #> [14,] -0.1666667 -0.20 -0.20 -0.2333333 -0.20 -0.20 #> [15,] -0.2000000 -0.24 -0.24 0.7200000 -0.24 -0.24 #> [16,] -0.2000000 -0.24 -0.24 -0.2800000 -0.24 -0.24 #> [17,] 0.7333333 0.68 -0.32 -0.3733333 -0.32 -0.32 #> [18,] 0.8333333 0.80 -0.20 -0.2333333 -0.20 -0.20 #> [19,] 0.8000000 0.76 0.76 -0.2800000 -0.24 -0.24 #> [20,] -0.1666667 -0.20 0.80 0.7666667 -0.20 -0.20 #> [21,] -0.2000000 -0.24 0.76 0.7200000 0.76 -0.24 #> [22,] 0.8000000 0.76 -0.24 0.7200000 0.76 0.76 #> [23,] 0.7666667 0.72 0.72 -0.3266667 0.72 0.72 #> [24,] -0.2000000 0.76 0.76 0.7200000 -0.24 0.76 #> [25,] -0.2000000 -0.24 0.76 0.7200000 0.76 -0.24 #> attr(,\"representation\") #> [1] \"modularity\" repr_graphon(g) #> [,1] [,2] [,3] [,4] [,5] [,6] #> [1,] 0.55555556 0.63333333 0.57777778 0.52777778 0.36507937 0.30952381 #> [2,] 0.63333333 0.60000000 0.70000000 0.65000000 0.68571429 0.34285714 #> [3,] 0.57777778 0.70000000 0.60000000 0.73333333 0.68571429 0.68571429 #> [4,] 0.52777778 0.65000000 0.73333333 0.66666667 0.77380952 0.61904762 #> [5,] 0.36507937 0.68571429 0.68571429 0.77380952 0.57142857 0.71428571 #> [6,] 0.30952381 0.34285714 0.68571429 0.61904762 0.71428571 0.57142857 #> [7,] 0.25000000 0.36666667 0.36666667 0.66666667 0.61904762 0.77380952 #> [8,] 0.18253968 0.17142857 0.34285714 0.30952381 0.57142857 0.57142857 #> [9,] 0.11111111 0.21111111 0.26666667 0.33333333 0.36507937 0.56349206 #> [10,] 0.00000000 0.00000000 0.18333333 0.16666667 0.30952381 0.30952381 #> [11,] 0.05555556 0.00000000 0.00000000 0.15476190 0.14285714 0.28571429 #> [12,] 0.00000000 0.00000000 0.00000000 0.05555556 0.18253968 0.23809524 #> [13,] 0.00000000 0.00000000 0.00000000 0.00000000 0.05555556 0.18253968 #> [14,] 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 #> [15,] 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 #> [16,] 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 #> [17,] 0.06250000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 #> [18,] 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 #> [19,] 0.11111111 0.05555556 0.00000000 0.00000000 0.00000000 0.00000000 #> [20,] 0.16666667 0.11111111 0.00000000 0.00000000 0.00000000 0.00000000 #> [21,] 0.22222222 0.11111111 0.00000000 0.00000000 0.00000000 0.00000000 #> [22,] 0.27777778 0.16666667 0.08333333 0.08333333 0.00000000 0.00000000 #> [23,] 0.55555556 0.26666667 0.08333333 0.08333333 0.15476190 0.00000000 #> [24,] 0.52222222 0.50000000 0.20000000 0.18333333 0.07142857 0.07142857 #> [25,] 0.50000000 0.47777778 0.26666667 0.25000000 0.23809524 0.18253968 #> [,7] [,8] [,9] [,10] [,11] [,12] #> [1,] 0.25000000 0.18253968 0.1111111 0.00000000 0.05555556 0.00000000 #> [2,] 0.36666667 0.17142857 0.2111111 0.00000000 0.00000000 0.00000000 #> [3,] 0.36666667 0.34285714 0.2666667 0.18333333 0.00000000 0.00000000 #> [4,] 0.66666667 0.30952381 0.3333333 0.16666667 0.15476190 0.05555556 #> [5,] 0.61904762 0.57142857 0.3650794 0.30952381 0.14285714 0.18253968 #> [6,] 0.77380952 0.57142857 0.5634921 0.30952381 0.28571429 0.23809524 #> [7,] 0.66666667 0.69047619 0.5833333 0.58333333 0.30952381 0.25000000 #> [8,] 0.69047619 0.57142857 0.6349206 0.61904762 0.57142857 0.30952381 #> [9,] 0.58333333 0.63492063 0.5555556 0.69444444 0.56349206 0.38888889 #> [10,] 0.58333333 0.61904762 0.6944444 0.66666667 0.61904762 0.52777778 #> [11,] 0.30952381 0.57142857 0.5634921 0.61904762 0.42857143 0.63492063 #> [12,] 0.25000000 0.30952381 0.3888889 0.52777778 0.63492063 0.55555556 #> [13,] 0.16666667 0.25396825 0.2777778 0.47222222 0.69047619 0.55555556 #> [14,] 0.05555556 0.12698413 0.2222222 0.19444444 0.30952381 0.44444444 #> [15,] 0.00000000 0.07142857 0.1111111 0.20833333 0.26785714 0.59722222 #> [16,] 0.00000000 0.00000000 0.1111111 0.11111111 0.25396825 0.33333333 #> [17,] 0.00000000 0.00000000 0.0625000 0.20833333 0.40178571 0.22916667 #> [18,] 0.00000000 0.00000000 0.0000000 0.00000000 0.05555556 0.16666667 #> [19,] 0.00000000 0.00000000 0.0000000 0.00000000 0.00000000 0.16666667 #> [20,] 0.00000000 0.00000000 0.0000000 0.00000000 0.05555556 0.05555556 #> [21,] 0.00000000 0.00000000 0.0000000 0.00000000 0.05555556 0.05555556 #> [22,] 0.00000000 0.00000000 0.0000000 0.00000000 0.00000000 0.00000000 #> [23,] 0.00000000 0.00000000 0.0000000 0.00000000 0.15476190 0.05555556 #> [24,] 0.00000000 0.00000000 0.0000000 0.00000000 0.10000000 0.00000000 #> [25,] 0.05555556 0.00000000 0.0000000 0.08333333 0.12698413 0.00000000 #> [,13] [,14] [,15] [,16] [,17] [,18] #> [1,] 0.00000000 0.00000000 0.00000000 0.00000000 0.0625000 0.00000000 #> [2,] 0.00000000 0.00000000 0.00000000 0.00000000 0.0000000 0.00000000 #> [3,] 0.00000000 0.00000000 0.00000000 0.00000000 0.0000000 0.00000000 #> [4,] 0.00000000 0.00000000 0.00000000 0.00000000 0.0000000 0.00000000 #> [5,] 0.05555556 0.00000000 0.00000000 0.00000000 0.0000000 0.00000000 #> [6,] 0.18253968 0.00000000 0.00000000 0.00000000 0.0000000 0.00000000 #> [7,] 0.16666667 0.05555556 0.00000000 0.00000000 0.0000000 0.00000000 #> [8,] 0.25396825 0.12698413 0.07142857 0.00000000 0.0000000 0.00000000 #> [9,] 0.27777778 0.22222222 0.11111111 0.11111111 0.0625000 0.00000000 #> [10,] 0.47222222 0.19444444 0.20833333 0.11111111 0.2083333 0.00000000 #> [11,] 0.69047619 0.30952381 0.26785714 0.25396825 0.4017857 0.05555556 #> [12,] 0.55555556 0.44444444 0.59722222 0.33333333 0.2291667 0.16666667 #> [13,] 0.55555556 0.55555556 0.65277778 0.44444444 0.2916667 0.27777778 #> [14,] 0.55555556 0.44444444 0.59722222 0.50000000 0.5833333 0.33333333 #> [15,] 0.65277778 0.59722222 0.75000000 0.59722222 0.6875000 0.29166667 #> [16,] 0.44444444 0.50000000 0.59722222 0.55555556 0.6388889 0.50000000 #> [17,] 0.29166667 0.58333333 0.68750000 0.63888889 0.3750000 0.57638889 #> [18,] 0.27777778 0.33333333 0.29166667 0.50000000 0.5763889 0.55555556 #> [19,] 0.27777778 0.27777778 0.23611111 0.44444444 0.6388889 0.55555556 #> [20,] 0.16666667 0.22222222 0.05555556 0.27777778 0.6458333 0.44444444 #> [21,] 0.16666667 0.22222222 0.05555556 0.27777778 0.6458333 0.44444444 #> [22,] 0.00000000 0.11111111 0.08333333 0.25000000 0.2916667 0.25000000 #> [23,] 0.05555556 0.11111111 0.20833333 0.25000000 0.1458333 0.30555556 #> [24,] 0.00000000 0.00000000 0.10000000 0.05555556 0.1250000 0.11111111 #> [25,] 0.00000000 0.00000000 0.00000000 0.00000000 0.2361111 0.16666667 #> [,19] [,20] [,21] [,22] [,23] [,24] #> [1,] 0.11111111 0.16666667 0.22222222 0.27777778 0.55555556 0.52222222 #> [2,] 0.05555556 0.11111111 0.11111111 0.16666667 0.26666667 0.50000000 #> [3,] 0.00000000 0.00000000 0.00000000 0.08333333 0.08333333 0.20000000 #> [4,] 0.00000000 0.00000000 0.00000000 0.08333333 0.08333333 0.18333333 #> [5,] 0.00000000 0.00000000 0.00000000 0.00000000 0.15476190 0.07142857 #> [6,] 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.07142857 #> [7,] 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 #> [8,] 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 #> [9,] 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 #> [10,] 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 #> [11,] 0.00000000 0.05555556 0.05555556 0.00000000 0.15476190 0.10000000 #> [12,] 0.16666667 0.05555556 0.05555556 0.00000000 0.05555556 0.00000000 #> [13,] 0.27777778 0.16666667 0.16666667 0.00000000 0.05555556 0.00000000 #> [14,] 0.27777778 0.22222222 0.22222222 0.11111111 0.11111111 0.00000000 #> [15,] 0.23611111 0.05555556 0.05555556 0.08333333 0.20833333 0.10000000 #> [16,] 0.44444444 0.27777778 0.27777778 0.25000000 0.25000000 0.05555556 #> [17,] 0.63888889 0.64583333 0.64583333 0.29166667 0.14583333 0.12500000 #> [18,] 0.55555556 0.44444444 0.44444444 0.25000000 0.30555556 0.11111111 #> [19,] 0.55555556 0.44444444 0.50000000 0.47222222 0.36111111 0.21111111 #> [20,] 0.44444444 0.33333333 0.38888889 0.52777778 0.58333333 0.36666667 #> [21,] 0.50000000 0.38888889 0.44444444 0.61111111 0.66666667 0.46666667 #> [22,] 0.47222222 0.52777778 0.61111111 0.50000000 0.66666667 0.63333333 #> [23,] 0.36111111 0.58333333 0.66666667 0.66666667 0.50000000 0.73333333 #> [24,] 0.21111111 0.36666667 0.46666667 0.63333333 0.73333333 0.80000000 #> [25,] 0.27777778 0.16666667 0.22222222 0.55555556 0.66666667 0.67777778 #> [,25] #> [1,] 0.50000000 #> [2,] 0.47777778 #> [3,] 0.26666667 #> [4,] 0.25000000 #> [5,] 0.23809524 #> [6,] 0.18253968 #> [7,] 0.05555556 #> [8,] 0.00000000 #> [9,] 0.00000000 #> [10,] 0.08333333 #> [11,] 0.12698413 #> [12,] 0.00000000 #> [13,] 0.00000000 #> [14,] 0.00000000 #> [15,] 0.00000000 #> [16,] 0.00000000 #> [17,] 0.23611111 #> [18,] 0.16666667 #> [19,] 0.27777778 #> [20,] 0.16666667 #> [21,] 0.22222222 #> [22,] 0.55555556 #> [23,] 0.66666667 #> [24,] 0.67777778 #> [25,] 0.44444444 #> attr(,\"representation\") #> [1] \"graphon\""},{"path":"https://astamm.github.io/nevada/reference/sample2_sbm.html","id":null,"dir":"Reference","previous_headings":"","what":"Two-Sample Stochastic Block Model Generator — sample2_sbm","title":"Two-Sample Stochastic Block Model Generator — sample2_sbm","text":"function generates two samples networks according stochastic block model (SBM). essentially wrapper around sample_sbm allows sample single network SBM.","code":""},{"path":"https://astamm.github.io/nevada/reference/sample2_sbm.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Two-Sample Stochastic Block Model Generator — sample2_sbm","text":"","code":"sample2_sbm(n, nv, p1, b1, p2 = p1, b2 = b1, seed = NULL)"},{"path":"https://astamm.github.io/nevada/reference/sample2_sbm.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Two-Sample Stochastic Block Model Generator — sample2_sbm","text":"n Integer scalar giving sample size. nv Integer scalar giving number vertices generated networks, common networks samples. p1 matrix giving Bernoulli rates 1st sample. KxK matrix, K number groups. probability creating edge vertices groups j given element (,j). undirected graphs, matrix must symmetric. b1 Numeric vector giving number vertices group first sample. sum vector must match number vertices. p2 matrix giving Bernoulli rates 2nd sample (default: 1st sample). KxK matrix, K number groups. probability creating edge vertices groups j given element (,j). undirected graphs, matrix must symmetric. b2 Numeric vector giving number vertices group second sample (default: 1st sample). sum vector must match number vertices. seed seed random number generator (default: NULL).","code":""},{"path":"https://astamm.github.io/nevada/reference/sample2_sbm.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Two-Sample Stochastic Block Model Generator — sample2_sbm","text":"length-2 list containing two samples stored nvd objects.","code":""},{"path":"https://astamm.github.io/nevada/reference/sample2_sbm.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Two-Sample Stochastic Block Model Generator — sample2_sbm","text":"","code":"n <- 10 p1 <- matrix( data = c(0.1, 0.4, 0.1, 0.4, 0.4, 0.4, 0.1, 0.4, 0.1, 0.1, 0.4, 0.4, 0.4, 0.4, 0.4, 0.4), nrow = 4, ncol = 4, byrow = TRUE ) p2 <- matrix( data = c(0.1, 0.4, 0.4, 0.4, 0.4, 0.4, 0.4, 0.4, 0.4, 0.4, 0.1, 0.1, 0.4, 0.4, 0.1, 0.4), nrow = 4, ncol = 4, byrow = TRUE ) sim <- sample2_sbm(n, 68, p1, c(17, 17, 17, 17), p2, seed = 1234)"},{"path":"https://astamm.github.io/nevada/reference/samplers.html","id":null,"dir":"Reference","previous_headings":"","what":"Graph samplers using edge distributions — samplers","title":"Graph samplers using edge distributions — samplers","text":"collection functions generate random graphs specified edge distribution.","code":""},{"path":"https://astamm.github.io/nevada/reference/samplers.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Graph samplers using edge distributions — samplers","text":"","code":"play_poisson(num_vertices, lambda = 1) rpois_network(n, num_vertices, lambda = 1) play_exponential(num_vertices, rate = 1) rexp_network(n, num_vertices, rate = 1) play_binomial(num_vertices, size = 1, prob = 0.5) rbinom_network(n, num_vertices, size = 1, prob = 0.5)"},{"path":"https://astamm.github.io/nevada/reference/samplers.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Graph samplers using edge distributions — samplers","text":"num_vertices Number vertices. lambda mean parameter Poisson distribution (default: 1). n Sample size. rate rate parameter exponential distribution (default: 1). size number trials binomial distribution (default: 1). prob probability success trial binomial distribution (default: 0.5).","code":""},{"path":"https://astamm.github.io/nevada/reference/samplers.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Graph samplers using edge distributions — samplers","text":"object class nvd containing sample graphs.","code":""},{"path":"https://astamm.github.io/nevada/reference/samplers.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Graph samplers using edge distributions — samplers","text":"","code":"nvd <- rexp_network(10, 68)"},{"path":"https://astamm.github.io/nevada/reference/statistics.html","id":null,"dir":"Reference","previous_headings":"","what":"Test Statistics for Network Populations — statistics","title":"Test Statistics for Network Populations — statistics","text":"collection functions provide statistics testing equality distribution samples networks.","code":""},{"path":"https://astamm.github.io/nevada/reference/statistics.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Test Statistics for Network Populations — statistics","text":"","code":"stat_student_euclidean(d, indices, ...) stat_welch_euclidean(d, indices, ...) stat_original_edge_count(d, indices, edge_count_prep, ...) stat_generalized_edge_count(d, indices, edge_count_prep, ...) stat_weighted_edge_count(d, indices, edge_count_prep, ...)"},{"path":"https://astamm.github.io/nevada/reference/statistics.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Test Statistics for Network Populations — statistics","text":"d Either matrix dimension \\((n1+n2)x(n1+n2)\\) containing distances elements two samples put together (distance-based statistics) concatenation lists matrix representations networks samples 1 2 Euclidean t-Statistics. indices vector dimension \\(n1\\) containing indices elements first sample. ... Extra parameters specific statistics. edge_count_prep list preprocessed data information used edge count statistics produced edge_count_global_variables.","code":""},{"path":"https://astamm.github.io/nevada/reference/statistics.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Test Statistics for Network Populations — statistics","text":"scalar giving value desired test statistic.","code":""},{"path":"https://astamm.github.io/nevada/reference/statistics.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Test Statistics for Network Populations — statistics","text":"details, three main categories statistics: Euclidean t-Statistics: Student stat_student_euclidean version equal variances Welch stat_welch_euclidean version unequal variances, Statistics based similarity graphs: 3 types edge count statistics.","code":""},{"path":"https://astamm.github.io/nevada/reference/statistics.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Test Statistics for Network Populations — statistics","text":"","code":"n1 <- 30L n2 <- 10L gnp_params <- list(n = 24L, p = 1/3) degree_params <- list(out_degree = rep(2, 24L), method = \"configuration\") x <- nvd(sample_size = n1, model = \"gnp\", !!!gnp_params) #> ℹ Calling the `tidygraph::play_gnp()` function with the following arguments: #> • n: 24 #> • p: 0.333333333333333 #> • directed: TRUE #> • loops: FALSE y <- nvd(sample_size = n2, model = \"degree\", !!!degree_params) #> ℹ Calling the `tidygraph::play_degree()` function with the following arguments: #> • out_degree: 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, …, 2, and 2 #> • method: configuration #> • in_degree: NULL r <- repr_nvd(x, y, representation = \"laplacian\") stat_student_euclidean(r, 1:n1) #> [1] 5.790399 stat_welch_euclidean(r, 1:n1) #> [1] 8.347264 d <- dist_nvd(x, y, representation = \"laplacian\", distance = \"frobenius\") ecp <- edge_count_global_variables(d, n1, k = 5L) stat_original_edge_count(d, 1:n1, edge_count_prep = ecp) #> [1] 9.701484 stat_generalized_edge_count(d, 1:n1, edge_count_prep = ecp) #> [1] 218.3131 stat_weighted_edge_count(d, 1:n1, edge_count_prep = ecp) #> [1] 14.7707"},{"path":"https://astamm.github.io/nevada/reference/subgraphs.html","id":null,"dir":"Reference","previous_headings":"","what":"Full, intra and inter subgraph generators — subgraphs","title":"Full, intra and inter subgraph generators — subgraphs","text":"collection functions extracting full, intra inter subgraphs graph given list vertex subsets.","code":""},{"path":"https://astamm.github.io/nevada/reference/subgraphs.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Full, intra and inter subgraph generators — subgraphs","text":"","code":"subgraph_full(g, vids) subgraph_intra(g, vids) subgraph_inter(g, vids)"},{"path":"https://astamm.github.io/nevada/reference/subgraphs.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Full, intra and inter subgraph generators — subgraphs","text":"g igraph object. vids list integer vectors identifying vertex subsets.","code":""},{"path":"https://astamm.github.io/nevada/reference/subgraphs.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Full, intra and inter subgraph generators — subgraphs","text":"igraph object storing subgraph type full, intra inter.","code":""},{"path":"https://astamm.github.io/nevada/reference/subgraphs.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Full, intra and inter subgraph generators — subgraphs","text":"","code":"g <- igraph::make_ring(10) g_full <- subgraph_full (g, list(1:3, 4:5, 8:10)) g_intra <- subgraph_intra(g, list(1:3, 4:5, 8:10)) g_inter <- subgraph_inter(g, list(1:3, 4:5, 8:10))"},{"path":"https://astamm.github.io/nevada/reference/test2_global.html","id":null,"dir":"Reference","previous_headings":"","what":"Global Two-Sample Test for Network-Valued Data — test2_global","title":"Global Two-Sample Test for Network-Valued Data — test2_global","text":"function carries hypothesis test null hypothesis two populations networks share underlying probabilistic distribution alternative hypothesis two populations come different distributions. test performed non-parametric fashion using permutational framework several statistics can used, together several choices network matrix representations distances networks.","code":""},{"path":"https://astamm.github.io/nevada/reference/test2_global.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Global Two-Sample Test for Network-Valued Data — test2_global","text":"","code":"test2_global( x, y, representation = c(\"adjacency\", \"laplacian\", \"modularity\", \"transitivity\"), distance = c(\"frobenius\", \"hamming\", \"spectral\", \"root-euclidean\"), stats = c(\"flipr:t_ip\", \"flipr:f_ip\"), B = 1000L, test = \"exact\", k = 5L, seed = NULL, ... )"},{"path":"https://astamm.github.io/nevada/reference/test2_global.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Global Two-Sample Test for Network-Valued Data — test2_global","text":"x Either object class nvd listing networks sample 1 distance matrix size \\(n_1 + n_2\\). y Either object class nvd listing networks sample 2 integer value specifying size sample 1 integer vector specifying indices observations belonging sample 1. representation string specifying desired type representation, among: \"adjacency\", \"laplacian\" \"modularity\". Defaults \"adjacency\". distance string specifying chosen distance calculating test statistic, among: \"hamming\", \"frobenius\", \"spectral\" \"root-euclidean\". Defaults \"frobenius\". stats character vector specifying chosen test statistic(s), among: \"original_edge_count\", \"generalized_edge_count\", \"weighted_edge_count\", \"student_euclidean\", \"welch_euclidean\" statistics based inter-point distances available flipr package: \"flipr:student_ip\", \"flipr:fisher_ip\", \"flipr:bg_ip\", \"flipr:energy_ip\", \"flipr:cq_ip\". Defaults c(\"flipr:student_ip\", \"flipr:fisher_ip\"). B number permutation tolerance. number lower 1, intended tolerance. Otherwise, intended number required permutations. Defaults 1000L. test character string specifying formula used compute permutation p-value. Choices \"estimate\", \"upper_bound\" \"exact\". Defaults \"exact\" provides exact tests. k integer specifying density minimum spanning tree used edge count statistics. Defaults 5L. seed integer specifying seed random generator result reproducibility. Defaults NULL. ... Extra arguments passed distance function.","code":""},{"path":"https://astamm.github.io/nevada/reference/test2_global.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Global Two-Sample Test for Network-Valued Data — test2_global","text":"list three components: value statistic original two samples, p-value resulting permutation test numeric vector storing values permuted statistics.","code":""},{"path":"https://astamm.github.io/nevada/reference/test2_global.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Global Two-Sample Test for Network-Valued Data — test2_global","text":"","code":"n <- 5L gnp_params <- list(n = 24L, p = 1/3) degree_params <- list(out_degree = rep(2, 24L), method = \"configuration\") # Two different models for the two populations x <- nvd(sample_size = n, model = \"gnp\", !!!gnp_params) #> ℹ Calling the `tidygraph::play_gnp()` function with the following arguments: #> • n: 24 #> • p: 0.333333333333333 #> • directed: TRUE #> • loops: FALSE y <- nvd(sample_size = n, model = \"degree\", !!!degree_params) #> ℹ Calling the `tidygraph::play_degree()` function with the following arguments: #> • out_degree: 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, …, 2, and 2 #> • method: configuration #> • in_degree: NULL t1 <- test2_global(x, y, representation = \"modularity\") #> ! Setting the seed for sampling permutations is mandatory for obtaining a continuous p-value function. Using `seed = 1234`. t1$pvalue #> [1] 0.002308242 # Same model for the two populations x <- nvd(sample_size = n, model = \"gnp\", !!!gnp_params) #> ℹ Calling the `tidygraph::play_gnp()` function with the following arguments: #> • n: 24 #> • p: 0.333333333333333 #> • directed: TRUE #> • loops: FALSE y <- nvd(sample_size = n, model = \"gnp\", !!!gnp_params) #> ℹ Calling the `tidygraph::play_gnp()` function with the following arguments: #> • n: 24 #> • p: 0.333333333333333 #> • directed: TRUE #> • loops: FALSE t2 <- test2_global(x, y, representation = \"modularity\") #> ! Setting the seed for sampling permutations is mandatory for obtaining a continuous p-value function. Using `seed = 1234`. t2$pvalue #> [1] 0.8234127"},{"path":"https://astamm.github.io/nevada/reference/test2_local.html","id":null,"dir":"Reference","previous_headings":"","what":"Local Two-Sample Test for Network-Valued Data — test2_local","title":"Local Two-Sample Test for Network-Valued Data — test2_local","text":"Local Two-Sample Test Network-Valued Data","code":""},{"path":"https://astamm.github.io/nevada/reference/test2_local.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Local Two-Sample Test for Network-Valued Data — test2_local","text":"","code":"test2_local( x, y, partition, representation = \"adjacency\", distance = \"frobenius\", stats = c(\"flipr:t_ip\", \"flipr:f_ip\"), B = 1000L, alpha = 0.05, test = \"exact\", k = 5L, seed = NULL, verbose = FALSE )"},{"path":"https://astamm.github.io/nevada/reference/test2_local.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Local Two-Sample Test for Network-Valued Data — test2_local","text":"x Either object class nvd listing networks sample 1 distance matrix size \\(n_1 + n_2\\). y Either object class nvd listing networks sample 2 integer value specifying size sample 1 integer vector specifying indices observations belonging sample 1. partition Either list integer vector specifying vertex memberships partition elements. representation string specifying desired type representation, among: \"adjacency\", \"laplacian\" \"modularity\". Defaults \"adjacency\". distance string specifying chosen distance calculating test statistic, among: \"hamming\", \"frobenius\", \"spectral\" \"root-euclidean\". Defaults \"frobenius\". stats character vector specifying chosen test statistic(s), among: \"original_edge_count\", \"generalized_edge_count\", \"weighted_edge_count\", \"student_euclidean\", \"welch_euclidean\" statistics based inter-point distances available flipr package: \"flipr:student_ip\", \"flipr:fisher_ip\", \"flipr:bg_ip\", \"flipr:energy_ip\", \"flipr:cq_ip\". Defaults c(\"flipr:student_ip\", \"flipr:fisher_ip\"). B number permutation tolerance. number lower 1, intended tolerance. Otherwise, intended number required permutations. Defaults 1000L. alpha Significance level hypothesis testing. set 1, function outputs properly adjusted p-values. lower 1, p-values lower alpha properly adjusted. Defaults 0.05. test character string specifying formula used compute permutation p-value. Choices \"estimate\", \"upper_bound\" \"exact\". Defaults \"exact\" provides exact tests. k integer specifying density minimum spanning tree used edge count statistics. Defaults 5L. seed integer specifying seed random generator result reproducibility. Defaults NULL. verbose Boolean specifying whether information intermediate tests printed process (default: FALSE).","code":""},{"path":"https://astamm.github.io/nevada/reference/test2_local.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Local Two-Sample Test for Network-Valued Data — test2_local","text":"length-2 list reporting adjusted p-values element partition intra- inter-tests.","code":""},{"path":"https://astamm.github.io/nevada/reference/test2_local.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Local Two-Sample Test for Network-Valued Data — test2_local","text":"","code":"n <- 5L p1 <- matrix( data = c(0.1, 0.4, 0.1, 0.4, 0.4, 0.4, 0.1, 0.4, 0.1, 0.1, 0.4, 0.4, 0.4, 0.4, 0.4, 0.4), nrow = 4, ncol = 4, byrow = TRUE ) p2 <- matrix( data = c(0.1, 0.4, 0.4, 0.4, 0.4, 0.4, 0.4, 0.4, 0.4, 0.4, 0.1, 0.1, 0.4, 0.4, 0.1, 0.4), nrow = 4, ncol = 4, byrow = TRUE ) sim <- sample2_sbm(n, 68, p1, c(17, 17, 17, 17), p2, seed = 1234) m <- as.integer(c(rep(1, 17), rep(2, 17), rep(3, 17), rep(4, 17))) test2_local(sim$x, sim$y, m, seed = 1234, alpha = 0.05, B = 19) #> $intra #> # A tibble: 4 × 3 #> E pvalue truncated #> #> 1 P1 0.548 TRUE #> 2 P2 0.548 TRUE #> 3 P3 0.0480 FALSE #> 4 P4 0.548 TRUE #> #> $inter #> # A tibble: 6 × 4 #> E1 E2 pvalue truncated #> #> 1 P1 P2 0.548 TRUE #> 2 P1 P3 0.0480 FALSE #> 3 P1 P4 0.548 TRUE #> 4 P2 P3 0.0480 FALSE #> 5 P2 P4 0.548 TRUE #> 6 P3 P4 0.0480 FALSE #>"},{"path":"https://astamm.github.io/nevada/reference/var2_nvd.html","id":null,"dir":"Reference","previous_headings":"","what":"Fréchet Variance of Network-Valued Data from Inter-Point Distances — var2_nvd","title":"Fréchet Variance of Network-Valued Data from Inter-Point Distances — var2_nvd","text":"function computes Fréchet variance using exclusively inter-point distances. , can accommodate pair representation distance.","code":""},{"path":"https://astamm.github.io/nevada/reference/var2_nvd.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Fréchet Variance of Network-Valued Data from Inter-Point Distances — var2_nvd","text":"","code":"var2_nvd(x, representation = \"adjacency\", distance = \"frobenius\")"},{"path":"https://astamm.github.io/nevada/reference/var2_nvd.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Fréchet Variance of Network-Valued Data from Inter-Point Distances — var2_nvd","text":"x nvd object listing sample networks. representation string specifying graph representation used. Choices adjacency, laplacian, modularity, graphon. Default adjacency. distance string specifying distance used. Possible choices : hamming, frobenius, spectral root-euclidean. Default frobenius.","code":""},{"path":"https://astamm.github.io/nevada/reference/var2_nvd.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Fréchet Variance of Network-Valued Data from Inter-Point Distances — var2_nvd","text":"positive scalar value evaluating variance based inter-point distances.","code":""},{"path":"https://astamm.github.io/nevada/reference/var2_nvd.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Fréchet Variance of Network-Valued Data from Inter-Point Distances — var2_nvd","text":"","code":"params <- list(n = 24L, p = 1/3) x <- nvd(sample_size = 1L, model = \"gnp\", !!!params) #> ℹ Calling the `tidygraph::play_gnp()` function with the following arguments: #> • n: 24 #> • p: 0.333333333333333 #> • directed: TRUE #> • loops: FALSE var2_nvd(x = x, representation = \"graphon\", distance = \"frobenius\") #> [1] NaN"},{"path":"https://astamm.github.io/nevada/reference/var_nvd.html","id":null,"dir":"Reference","previous_headings":"","what":"Fréchet Variance of Network-Valued Data Around a Given Network — var_nvd","title":"Fréchet Variance of Network-Valued Data Around a Given Network — var_nvd","text":"function computes Fréchet variance around specified network observed sample network-valued random variables according specified distance. cases, user willing compute sample variance, case Fréchet variance evaluated w.r.t. sample Fréchet mean. case, important user indicates distance one (s)used separately compute sample Fréchet mean. function can also used function minimized order find Fréchet mean given distance.","code":""},{"path":"https://astamm.github.io/nevada/reference/var_nvd.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Fréchet Variance of Network-Valued Data Around a Given Network — var_nvd","text":"","code":"var_nvd(x, x0, weights = rep(1, length(x)), distance = \"frobenius\")"},{"path":"https://astamm.github.io/nevada/reference/var_nvd.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Fréchet Variance of Network-Valued Data Around a Given Network — var_nvd","text":"x nvd object listing sample networks. x0 network already matrix representation around calculate variance (usually Fréchet mean necessarily). Note chosen matrix representation extracted parameter. weights numeric vector specifying weights observation (default: equally weighted). distance string specifying distance used. Possible choices : hamming, frobenius, spectral root-euclidean. Default frobenius. Fréchet mean used x0 parameter, distance match one used compute mean. currently checked.","code":""},{"path":"https://astamm.github.io/nevada/reference/var_nvd.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Fréchet Variance of Network-Valued Data Around a Given Network — var_nvd","text":"positive scalar value evaluating amount variability sample around specified network.","code":""},{"path":"https://astamm.github.io/nevada/reference/var_nvd.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Fréchet Variance of Network-Valued Data Around a Given Network — var_nvd","text":"","code":"params <- list(n = 24L, p = 1/3) x <- nvd(sample_size = 1L, model = \"gnp\", !!!params) #> ℹ Calling the `tidygraph::play_gnp()` function with the following arguments: #> • n: 24 #> • p: 0.333333333333333 #> • directed: TRUE #> • loops: FALSE m <- mean(x) var_nvd(x = x, x0 = m, distance = \"frobenius\") #> [1] 0"},{"path":[]},{"path":"https://astamm.github.io/nevada/news/index.html","id":"nevada-020","dir":"Changelog","previous_headings":"","what":"nevada 0.2.0","title":"nevada 0.2.0","text":"CRAN release: 2023-09-03 Improved nvd constructor. Updated GHA scripts. Added tSNE UMAP viz. Added support graphs different sizes /unlabeled graphs. Added support distance matrices test functions. Added support parallelization via future framework furrr.","code":""},{"path":"https://astamm.github.io/nevada/news/index.html","id":"nevada-010","dir":"Changelog","previous_headings":"","what":"nevada 0.1.0","title":"nevada 0.1.0","text":"CRAN release: 2021-09-25 Initial release. Added NEWS.md file track changes package.","code":""}] +[{"path":"https://astamm.github.io/nevada/LICENSE.html","id":null,"dir":"","previous_headings":"","what":"GNU General Public License","title":"GNU General Public License","text":"Version 3, 29 June 2007Copyright © 2007 Free Software Foundation, Inc.  Everyone permitted copy distribute verbatim copies license document, changing allowed.","code":""},{"path":"https://astamm.github.io/nevada/LICENSE.html","id":"preamble","dir":"","previous_headings":"","what":"Preamble","title":"GNU General Public License","text":"GNU General Public License free, copyleft license software kinds works. licenses software practical works designed take away freedom share change works. contrast, GNU General Public License intended guarantee freedom share change versions program–make sure remains free software users. , Free Software Foundation, use GNU General Public License software; applies also work released way authors. can apply programs, . speak free software, referring freedom, price. 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Definitions","title":"GNU General Public License","text":"“License” refers version 3 GNU General Public License. “Copyright” also means copyright-like laws apply kinds works, semiconductor masks. “Program” refers copyrightable work licensed License. licensee addressed “”. “Licensees” “recipients” may individuals organizations. “modify” work means copy adapt part work fashion requiring copyright permission, making exact copy. resulting work called “modified version” earlier work work “based ” earlier work. “covered work” means either unmodified Program work based Program. “propagate” work means anything , without permission, make directly secondarily liable infringement applicable copyright law, except executing computer modifying private copy. Propagation includes copying, distribution (without modification), making available public, countries activities well. “convey” work means kind propagation enables parties make receive copies. 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Protecting Users’ Legal Rights From Anti-Circumvention Law","title":"GNU General Public License","text":"covered work shall deemed part effective technological measure applicable law fulfilling obligations article 11 WIPO copyright treaty adopted 20 December 1996, similar laws prohibiting restricting circumvention measures. convey covered work, waive legal power forbid circumvention technological measures extent circumvention effected exercising rights License respect covered work, disclaim intention limit operation modification work means enforcing, work’s users, third parties’ legal rights forbid circumvention technological measures.","code":""},{"path":"https://astamm.github.io/nevada/LICENSE.html","id":"id_4-conveying-verbatim-copies","dir":"","previous_headings":"TERMS AND CONDITIONS","what":"4. 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Termination","title":"GNU General Public License","text":"may propagate modify covered work except expressly provided License. attempt otherwise propagate modify void, automatically terminate rights License (including patent licenses granted third paragraph section 11). However, cease violation License, license particular copyright holder reinstated () provisionally, unless copyright holder explicitly finally terminates license, (b) permanently, copyright holder fails notify violation reasonable means prior 60 days cessation. Moreover, license particular copyright holder reinstated permanently copyright holder notifies violation reasonable means, first time received notice violation License (work) copyright holder, cure violation prior 30 days receipt notice. 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Interpretation of Sections 15 and 16","title":"GNU General Public License","text":"disclaimer warranty limitation liability provided given local legal effect according terms, reviewing courts shall apply local law closely approximates absolute waiver civil liability connection Program, unless warranty assumption liability accompanies copy Program return fee. END TERMS CONDITIONS","code":""},{"path":"https://astamm.github.io/nevada/LICENSE.html","id":"how-to-apply-these-terms-to-your-new-programs","dir":"","previous_headings":"","what":"How to Apply These Terms to Your New Programs","title":"GNU General Public License","text":"develop new program, want greatest possible use public, best way achieve make free software everyone can redistribute change terms. , attach following notices program. safest attach start source file effectively state exclusion warranty; file least “copyright” line pointer full notice found. Also add information contact electronic paper mail. program terminal interaction, make output short notice like starts interactive mode: hypothetical commands show w show c show appropriate parts General Public License. course, program’s commands might different; GUI interface, use “box”. also get employer (work programmer) school, , sign “copyright disclaimer” program, necessary. information , apply follow GNU GPL, see . GNU General Public License permit incorporating program proprietary programs. program subroutine library, may consider useful permit linking proprietary applications library. want , use GNU Lesser General Public License instead License. first, please read .","code":" Copyright (C) This program is free software: you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation, either version 3 of the License, or (at your option) any later version. This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with this program. If not, see . Copyright (C) This program comes with ABSOLUTELY NO WARRANTY; for details type 'show w'. This is free software, and you are welcome to redistribute it under certain conditions; type 'show c' for details."},{"path":"https://astamm.github.io/nevada/articles/nevada.html","id":"the-nvd-class-for-network-valued-data","dir":"Articles","previous_headings":"","what":"The nvd class for network-valued data","title":"nevada","text":"nevada, network-valued data stored object class nvd, basically list igraph objects. provide: constructor nvd() allows user simulate samples networks using popular models igraph. Currently, one can use: stochastic block model, kk-regular model, GNP model, small-world model, PA model, Poisson model, binomial model. constructor simulates networks 25 nodes. function as_nvd() coerce lists igraph objects object class nvd.","code":""},{"path":"https://astamm.github.io/nevada/articles/nevada.html","id":"network-representation","dir":"Articles","previous_headings":"","what":"Network representation","title":"nevada","text":"currently 3 possible matrix representations network. Let GG network NN nodes. NN x NN matrix WW adjacency matrix GG element WijW_{ij} indicates edge vertex ii vertex jj: Wij={wi,j,(,j)∈E weight wi,j0,otherwise. W_{ij}= \\begin{cases} w_{,j}, & \\mbox{} (,j) \\E \\mbox{ weight } w_{,j}\\\\ 0, & \\mbox{otherwise.} \\end{cases} nevada, representation can achieved repr_adjacency(). Laplacian matrix LL network GG defined following way: L=D(W)−W, L = D(W) - W, D(W)D(W) diagonal matrix whose ii-th diagonal element degree vertex ii. nevada, representation can achieved repr_laplacian(). elements modularity matrix BB given Bij=Wij−didj2m, B_{ij} = W_{ij} - \\frac{d_i d_j}{2m}, did_i djd_j degrees vertices ii jj respectively, mm total number edges network. nevada, representation can achieved repr_modularity(). Instead going every single network sample make representation, nevada provides repr_nvd() function exactly object class nvd.","code":"x <- nvd(sample_size = 3L, model = \"gnp\", n = 24L, p = 1/3) #> ℹ Calling the `tidygraph::play_gnp()` function with the following arguments: #> • n: 24 #> • p: 0.333333333333333 #> • directed: TRUE #> • loops: FALSE repr_nvd(x, representation = \"laplacian\") #> [[1]] #> [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12] [,13] #> [1,] 7 0 0 0 0 0 0 0 0 0 -1 0 -1 #> [2,] 0 8 0 0 0 -1 0 -1 -1 -1 -1 0 0 #> [3,] 0 0 5 0 0 0 0 0 0 0 -1 0 0 #> [4,] 0 0 -1 8 -1 0 -1 0 -1 0 0 0 0 #> [5,] 0 0 -1 -1 10 -1 -1 0 0 0 0 0 0 #> [6,] 0 -1 0 -1 0 6 0 0 0 0 0 0 -1 #> [7,] 0 0 0 -1 -1 0 4 0 0 0 -1 0 0 #> [8,] 0 0 0 -1 -1 -1 0 8 0 0 0 -1 0 #> [9,] 0 0 0 0 0 -1 0 -1 5 0 0 -1 0 #> [10,] 0 -1 0 0 0 -1 -1 -1 0 7 -1 0 0 #> [11,] 0 0 0 0 -1 0 -1 0 -1 0 9 -1 0 #> [12,] 0 -1 0 -1 0 0 0 0 0 -1 0 6 0 #> [13,] 0 0 0 0 0 0 0 -1 0 0 0 -1 6 #> [14,] -1 0 -1 0 -1 -1 0 -1 0 -1 -1 0 0 #> [15,] -1 0 0 0 0 0 0 -1 0 0 -1 0 0 #> [16,] 0 0 0 -1 0 0 0 0 -1 -1 -1 0 0 #> [17,] 0 0 -1 -1 0 -1 -1 0 -1 0 0 0 0 #> [18,] -1 0 0 0 0 0 0 -1 0 0 0 -1 -1 #> [19,] 0 0 0 0 -1 0 0 0 0 0 0 -1 -1 #> [20,] -1 -1 0 -1 -1 -1 0 0 0 0 0 -1 -1 #> [21,] 0 0 -1 0 0 0 0 0 0 -1 0 0 -1 #> [22,] 0 0 0 0 0 0 0 0 0 -1 0 -1 0 #> [23,] 0 -1 0 0 0 0 0 0 0 0 -1 0 0 #> [24,] 0 0 0 0 -1 -1 -1 -1 0 0 0 0 0 #> [,14] [,15] [,16] [,17] [,18] [,19] [,20] [,21] [,22] [,23] [,24] #> [1,] -1 0 0 0 -1 -1 -1 0 0 -1 0 #> [2,] 0 -1 0 0 0 0 0 0 -1 -1 0 #> [3,] 0 0 0 -1 -1 -1 -1 0 0 0 0 #> [4,] 0 -1 0 0 0 -1 0 0 -1 0 -1 #> [5,] -1 -1 0 0 -1 -1 0 0 -1 -1 0 #> [6,] -1 0 -1 0 0 0 -1 0 0 0 0 #> [7,] 0 0 0 0 0 0 -1 0 0 0 0 #> [8,] 0 -1 0 0 -1 0 0 0 -1 0 -1 #> [9,] 0 0 -1 0 0 0 0 0 0 0 -1 #> [10,] 0 0 0 0 0 -1 0 0 0 -1 0 #> [11,] -1 0 0 0 0 -1 0 -1 -1 -1 0 #> [12,] -1 -1 -1 0 0 0 0 0 0 0 0 #> [13,] -1 0 -1 0 0 0 -1 0 0 -1 0 #> [14,] 12 -1 0 0 -1 -1 0 0 0 -1 -1 #> [15,] -1 8 0 0 -1 -1 0 -1 -1 0 0 #> [16,] 0 -1 8 -1 0 0 0 -1 -1 0 0 #> [17,] 0 0 0 8 0 -1 0 0 0 -1 -1 #> [18,] 0 0 0 0 6 -1 0 0 0 0 -1 #> [19,] -1 0 0 0 0 8 -1 -1 -1 -1 0 #> [20,] 0 0 -1 -1 0 -1 11 0 0 0 -1 #> [21,] 0 0 0 -1 0 0 0 6 -1 -1 0 #> [22,] 0 0 0 0 -1 0 -1 0 4 0 0 #> [23,] 0 0 0 -1 -1 0 -1 0 0 6 -1 #> [24,] 0 -1 -1 0 -1 0 0 0 0 0 7 #> attr(,\"representation\") #> [1] \"laplacian\" #> #> [[2]] #> [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12] [,13] #> [1,] 6 0 0 0 0 0 0 -1 0 0 0 -1 -1 #> [2,] 0 3 0 -1 0 0 0 0 0 -1 0 0 0 #> [3,] -1 -1 6 0 0 0 -1 0 -1 0 0 0 -1 #> [4,] 0 0 -1 8 -1 0 -1 0 0 0 0 -1 0 #> [5,] 0 -1 0 -1 5 -1 0 0 0 0 0 -1 0 #> [6,] 0 -1 0 0 0 7 0 0 0 -1 0 -1 0 #> [7,] -1 -1 0 0 0 -1 8 0 0 0 -1 0 0 #> [8,] 0 -1 -1 0 0 0 -1 8 0 0 0 0 -1 #> [9,] 0 0 0 -1 -1 -1 0 0 9 0 0 0 -1 #> [10,] 0 0 -1 0 0 -1 0 0 0 6 0 -1 -1 #> [11,] 0 0 -1 -1 0 0 -1 -1 0 0 9 0 0 #> [12,] 0 0 0 0 0 0 0 -1 0 -1 0 6 -1 #> [13,] 0 -1 -1 -1 0 0 0 -1 -1 0 0 -1 8 #> [14,] -1 -1 0 0 0 0 -1 -1 -1 0 0 0 -1 #> [15,] 0 0 0 0 0 0 0 0 0 -1 -1 0 0 #> [16,] 0 0 -1 0 0 0 -1 -1 0 0 -1 0 -1 #> [17,] -1 0 0 0 0 0 -1 0 0 0 -1 -1 -1 #> [18,] -1 0 -1 0 0 0 -1 -1 0 -1 0 0 0 #> [19,] 0 0 0 0 0 0 0 0 0 0 0 -1 0 #> [20,] -1 0 0 0 0 0 -1 -1 0 -1 0 0 -1 #> [21,] 0 0 0 -1 0 0 0 0 0 -1 0 0 0 #> [22,] -1 -1 -1 0 0 0 0 0 0 0 0 -1 0 #> [23,] -1 0 0 0 0 0 0 -1 -1 -1 -1 -1 0 #> [24,] -1 0 -1 0 0 0 -1 -1 0 0 0 0 0 #> [,14] [,15] [,16] [,17] [,18] [,19] [,20] [,21] [,22] [,23] [,24] #> [1,] 0 -1 -1 0 0 -1 0 0 0 0 0 #> [2,] 0 0 0 0 0 0 -1 0 0 0 0 #> [3,] 0 0 -1 0 0 0 0 0 0 0 0 #> [4,] 0 0 0 -1 -1 0 -1 0 0 -1 0 #> [5,] 0 -1 0 0 0 0 0 0 0 0 0 #> [6,] -1 0 -1 0 0 0 0 0 -1 0 -1 #> [7,] 0 -1 0 -1 0 0 -1 0 0 0 -1 #> [8,] 0 0 -1 0 -1 -1 -1 0 0 0 0 #> [9,] -1 -1 -1 0 0 0 -1 0 0 0 -1 #> [10,] 0 -1 0 0 0 0 -1 0 0 0 0 #> [11,] 0 -1 0 -1 0 0 -1 0 -1 -1 0 #> [12,] 0 -1 -1 0 0 0 0 0 0 -1 0 #> [13,] 0 0 0 0 0 -1 0 -1 0 0 0 #> [14,] 9 -1 0 0 0 0 0 0 -1 0 -1 #> [15,] -1 4 0 0 -1 0 0 0 0 0 0 #> [16,] 0 0 8 -1 0 -1 0 0 0 0 -1 #> [17,] 0 -1 -1 11 0 -1 -1 -1 0 -1 0 #> [18,] 0 0 0 0 6 0 0 0 0 -1 0 #> [19,] -1 0 0 0 -1 4 0 0 0 -1 0 #> [20,] -1 0 -1 0 0 0 9 0 0 -1 -1 #> [21,] 0 0 0 -1 0 0 0 4 0 -1 0 #> [22,] -1 0 0 0 -1 -1 -1 0 9 -1 0 #> [23,] 0 0 0 -1 0 -1 0 -1 0 10 -1 #> [24,] 0 -1 0 -1 0 0 0 -1 0 0 7 #> attr(,\"representation\") #> [1] \"laplacian\" #> #> [[3]] #> [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12] [,13] #> [1,] 7 0 -1 -1 0 0 0 0 0 -1 -1 0 0 #> [2,] 0 7 0 -1 -1 -1 -1 0 -1 0 -1 0 0 #> [3,] -1 0 8 -1 0 -1 0 0 0 -1 0 0 0 #> [4,] 0 0 0 10 -1 -1 0 -1 -1 0 0 0 0 #> [5,] -1 -1 0 0 7 -1 0 -1 0 0 0 0 0 #> [6,] 0 -1 0 0 -1 8 -1 0 -1 0 0 0 0 #> [7,] 0 0 0 0 0 -1 3 0 0 0 0 0 0 #> [8,] 0 0 0 0 0 0 0 7 -1 0 -1 0 0 #> [9,] 0 -1 0 0 -1 0 -1 -1 11 -1 -1 0 -1 #> [10,] 0 -1 -1 0 0 0 0 -1 -1 8 0 0 0 #> [11,] 0 0 0 -1 0 -1 0 0 0 0 8 0 -1 #> [12,] -1 0 -1 -1 0 -1 -1 0 0 -1 -1 14 -1 #> [13,] 0 -1 0 -1 -1 0 0 0 0 0 0 0 6 #> [14,] 0 0 0 -1 0 0 0 0 -1 0 -1 0 0 #> [15,] 0 -1 0 0 -1 0 0 -1 0 -1 0 0 -1 #> [16,] -1 0 0 0 0 -1 0 -1 -1 -1 -1 0 0 #> [17,] 0 0 0 0 0 -1 0 0 0 0 0 0 0 #> [18,] 0 0 0 -1 0 -1 0 0 0 0 0 0 0 #> [19,] 0 -1 0 -1 0 0 -1 0 -1 0 0 -1 -1 #> [20,] -1 0 -1 0 -1 0 0 -1 -1 0 0 0 0 #> [21,] -1 0 -1 -1 -1 0 0 0 0 0 -1 0 0 #> [22,] -1 -1 0 0 0 -1 -1 0 0 0 0 -1 -1 #> [23,] 0 -1 -1 0 -1 0 -1 -1 0 0 0 0 0 #> [24,] 0 -1 0 0 0 0 0 0 0 0 -1 0 0 #> [,14] [,15] [,16] [,17] [,18] [,19] [,20] [,21] [,22] [,23] [,24] #> [1,] 0 0 -1 -1 0 0 0 0 0 0 -1 #> [2,] 0 0 0 0 0 0 0 0 -1 0 0 #> [3,] -1 0 0 -1 0 -1 0 0 0 -1 0 #> [4,] -1 -1 -1 -1 -1 -1 0 0 0 0 0 #> [5,] 0 0 0 -1 0 0 0 -1 0 0 -1 #> [6,] 0 0 0 -1 0 -1 -1 0 0 -1 0 #> [7,] 0 0 0 0 0 0 0 -1 0 0 -1 #> [8,] -1 0 -1 0 0 0 -1 0 -1 -1 0 #> [9,] 0 0 -1 0 0 0 -1 -1 0 0 -1 #> [10,] 0 0 0 -1 -1 0 0 0 -1 -1 0 #> [11,] -1 0 0 -1 0 0 -1 -1 0 -1 0 #> [12,] -1 0 0 -1 -1 0 -1 0 -1 0 -1 #> [13,] 0 0 -1 0 -1 0 0 0 0 -1 0 #> [14,] 7 0 -1 0 -1 0 0 0 -1 -1 0 #> [15,] 0 10 0 0 0 -1 -1 0 -1 -1 -1 #> [16,] -1 0 10 0 -1 0 0 0 -1 -1 0 #> [17,] 0 0 0 5 0 0 -1 -1 0 -1 -1 #> [18,] -1 0 0 -1 4 0 0 0 0 0 0 #> [19,] 0 0 0 0 0 7 -1 0 0 0 0 #> [20,] -1 0 0 -1 0 0 9 -1 -1 0 0 #> [21,] -1 -1 0 0 -1 0 -1 11 -1 0 -1 #> [22,] 0 0 0 0 0 0 -1 0 7 0 0 #> [23,] -1 0 0 -1 0 -1 0 0 0 8 0 #> [24,] 0 -1 0 0 0 0 0 0 -1 -1 5 #> attr(,\"representation\") #> [1] \"laplacian\""},{"path":"https://astamm.github.io/nevada/articles/nevada.html","id":"adjacency-matrix","dir":"Articles","previous_headings":"","what":"Adjacency matrix","title":"nevada","text":"NN x NN matrix WW adjacency matrix GG element WijW_{ij} indicates edge vertex ii vertex jj: Wij={wi,j,(,j)∈E weight wi,j0,otherwise. W_{ij}= \\begin{cases} w_{,j}, & \\mbox{} (,j) \\E \\mbox{ weight } w_{,j}\\\\ 0, & \\mbox{otherwise.} \\end{cases} nevada, representation can achieved repr_adjacency().","code":""},{"path":"https://astamm.github.io/nevada/articles/nevada.html","id":"laplacian-matrix","dir":"Articles","previous_headings":"","what":"Laplacian matrix","title":"nevada","text":"Laplacian matrix LL network GG defined following way: L=D(W)−W, L = D(W) - W, D(W)D(W) diagonal matrix whose ii-th diagonal element degree vertex ii. nevada, representation can achieved repr_laplacian().","code":""},{"path":"https://astamm.github.io/nevada/articles/nevada.html","id":"modularity-matrix","dir":"Articles","previous_headings":"","what":"Modularity matrix","title":"nevada","text":"elements modularity matrix BB given Bij=Wij−didj2m, B_{ij} = W_{ij} - \\frac{d_i d_j}{2m}, did_i djd_j degrees vertices ii jj respectively, mm total number edges network. nevada, representation can achieved repr_modularity().","code":""},{"path":"https://astamm.github.io/nevada/articles/nevada.html","id":"choosing-a-representation-for-an-object-of-class-nvd","dir":"Articles","previous_headings":"","what":"Choosing a representation for an object of class nvd","title":"nevada","text":"Instead going every single network sample make representation, nevada provides repr_nvd() function exactly object class nvd.","code":"x <- nvd(sample_size = 3L, model = \"gnp\", n = 24L, p = 1/3) #> ℹ Calling the `tidygraph::play_gnp()` function with the following arguments: #> • n: 24 #> • p: 0.333333333333333 #> • directed: TRUE #> • loops: FALSE repr_nvd(x, representation = \"laplacian\") #> [[1]] #> [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12] [,13] #> [1,] 7 0 0 0 0 0 0 0 0 0 -1 0 -1 #> [2,] 0 8 0 0 0 -1 0 -1 -1 -1 -1 0 0 #> [3,] 0 0 5 0 0 0 0 0 0 0 -1 0 0 #> [4,] 0 0 -1 8 -1 0 -1 0 -1 0 0 0 0 #> [5,] 0 0 -1 -1 10 -1 -1 0 0 0 0 0 0 #> [6,] 0 -1 0 -1 0 6 0 0 0 0 0 0 -1 #> [7,] 0 0 0 -1 -1 0 4 0 0 0 -1 0 0 #> [8,] 0 0 0 -1 -1 -1 0 8 0 0 0 -1 0 #> [9,] 0 0 0 0 0 -1 0 -1 5 0 0 -1 0 #> [10,] 0 -1 0 0 0 -1 -1 -1 0 7 -1 0 0 #> [11,] 0 0 0 0 -1 0 -1 0 -1 0 9 -1 0 #> [12,] 0 -1 0 -1 0 0 0 0 0 -1 0 6 0 #> [13,] 0 0 0 0 0 0 0 -1 0 0 0 -1 6 #> [14,] -1 0 -1 0 -1 -1 0 -1 0 -1 -1 0 0 #> [15,] -1 0 0 0 0 0 0 -1 0 0 -1 0 0 #> [16,] 0 0 0 -1 0 0 0 0 -1 -1 -1 0 0 #> [17,] 0 0 -1 -1 0 -1 -1 0 -1 0 0 0 0 #> [18,] -1 0 0 0 0 0 0 -1 0 0 0 -1 -1 #> [19,] 0 0 0 0 -1 0 0 0 0 0 0 -1 -1 #> [20,] -1 -1 0 -1 -1 -1 0 0 0 0 0 -1 -1 #> [21,] 0 0 -1 0 0 0 0 0 0 -1 0 0 -1 #> [22,] 0 0 0 0 0 0 0 0 0 -1 0 -1 0 #> [23,] 0 -1 0 0 0 0 0 0 0 0 -1 0 0 #> [24,] 0 0 0 0 -1 -1 -1 -1 0 0 0 0 0 #> [,14] [,15] [,16] [,17] [,18] [,19] [,20] [,21] [,22] [,23] [,24] #> [1,] -1 0 0 0 -1 -1 -1 0 0 -1 0 #> [2,] 0 -1 0 0 0 0 0 0 -1 -1 0 #> [3,] 0 0 0 -1 -1 -1 -1 0 0 0 0 #> [4,] 0 -1 0 0 0 -1 0 0 -1 0 -1 #> [5,] -1 -1 0 0 -1 -1 0 0 -1 -1 0 #> [6,] -1 0 -1 0 0 0 -1 0 0 0 0 #> [7,] 0 0 0 0 0 0 -1 0 0 0 0 #> [8,] 0 -1 0 0 -1 0 0 0 -1 0 -1 #> [9,] 0 0 -1 0 0 0 0 0 0 0 -1 #> [10,] 0 0 0 0 0 -1 0 0 0 -1 0 #> [11,] -1 0 0 0 0 -1 0 -1 -1 -1 0 #> [12,] -1 -1 -1 0 0 0 0 0 0 0 0 #> [13,] -1 0 -1 0 0 0 -1 0 0 -1 0 #> [14,] 12 -1 0 0 -1 -1 0 0 0 -1 -1 #> [15,] -1 8 0 0 -1 -1 0 -1 -1 0 0 #> [16,] 0 -1 8 -1 0 0 0 -1 -1 0 0 #> [17,] 0 0 0 8 0 -1 0 0 0 -1 -1 #> [18,] 0 0 0 0 6 -1 0 0 0 0 -1 #> [19,] -1 0 0 0 0 8 -1 -1 -1 -1 0 #> [20,] 0 0 -1 -1 0 -1 11 0 0 0 -1 #> [21,] 0 0 0 -1 0 0 0 6 -1 -1 0 #> [22,] 0 0 0 0 -1 0 -1 0 4 0 0 #> [23,] 0 0 0 -1 -1 0 -1 0 0 6 -1 #> [24,] 0 -1 -1 0 -1 0 0 0 0 0 7 #> attr(,\"representation\") #> [1] \"laplacian\" #> #> [[2]] #> [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12] [,13] #> [1,] 6 0 0 0 0 0 0 -1 0 0 0 -1 -1 #> [2,] 0 3 0 -1 0 0 0 0 0 -1 0 0 0 #> [3,] -1 -1 6 0 0 0 -1 0 -1 0 0 0 -1 #> [4,] 0 0 -1 8 -1 0 -1 0 0 0 0 -1 0 #> [5,] 0 -1 0 -1 5 -1 0 0 0 0 0 -1 0 #> [6,] 0 -1 0 0 0 7 0 0 0 -1 0 -1 0 #> [7,] -1 -1 0 0 0 -1 8 0 0 0 -1 0 0 #> [8,] 0 -1 -1 0 0 0 -1 8 0 0 0 0 -1 #> [9,] 0 0 0 -1 -1 -1 0 0 9 0 0 0 -1 #> [10,] 0 0 -1 0 0 -1 0 0 0 6 0 -1 -1 #> [11,] 0 0 -1 -1 0 0 -1 -1 0 0 9 0 0 #> [12,] 0 0 0 0 0 0 0 -1 0 -1 0 6 -1 #> [13,] 0 -1 -1 -1 0 0 0 -1 -1 0 0 -1 8 #> [14,] -1 -1 0 0 0 0 -1 -1 -1 0 0 0 -1 #> [15,] 0 0 0 0 0 0 0 0 0 -1 -1 0 0 #> [16,] 0 0 -1 0 0 0 -1 -1 0 0 -1 0 -1 #> [17,] -1 0 0 0 0 0 -1 0 0 0 -1 -1 -1 #> [18,] -1 0 -1 0 0 0 -1 -1 0 -1 0 0 0 #> [19,] 0 0 0 0 0 0 0 0 0 0 0 -1 0 #> [20,] -1 0 0 0 0 0 -1 -1 0 -1 0 0 -1 #> [21,] 0 0 0 -1 0 0 0 0 0 -1 0 0 0 #> [22,] -1 -1 -1 0 0 0 0 0 0 0 0 -1 0 #> [23,] -1 0 0 0 0 0 0 -1 -1 -1 -1 -1 0 #> [24,] -1 0 -1 0 0 0 -1 -1 0 0 0 0 0 #> [,14] [,15] [,16] [,17] [,18] [,19] [,20] [,21] [,22] [,23] [,24] #> [1,] 0 -1 -1 0 0 -1 0 0 0 0 0 #> [2,] 0 0 0 0 0 0 -1 0 0 0 0 #> [3,] 0 0 -1 0 0 0 0 0 0 0 0 #> [4,] 0 0 0 -1 -1 0 -1 0 0 -1 0 #> [5,] 0 -1 0 0 0 0 0 0 0 0 0 #> [6,] -1 0 -1 0 0 0 0 0 -1 0 -1 #> [7,] 0 -1 0 -1 0 0 -1 0 0 0 -1 #> [8,] 0 0 -1 0 -1 -1 -1 0 0 0 0 #> [9,] -1 -1 -1 0 0 0 -1 0 0 0 -1 #> [10,] 0 -1 0 0 0 0 -1 0 0 0 0 #> [11,] 0 -1 0 -1 0 0 -1 0 -1 -1 0 #> [12,] 0 -1 -1 0 0 0 0 0 0 -1 0 #> [13,] 0 0 0 0 0 -1 0 -1 0 0 0 #> [14,] 9 -1 0 0 0 0 0 0 -1 0 -1 #> [15,] -1 4 0 0 -1 0 0 0 0 0 0 #> [16,] 0 0 8 -1 0 -1 0 0 0 0 -1 #> [17,] 0 -1 -1 11 0 -1 -1 -1 0 -1 0 #> [18,] 0 0 0 0 6 0 0 0 0 -1 0 #> [19,] -1 0 0 0 -1 4 0 0 0 -1 0 #> [20,] -1 0 -1 0 0 0 9 0 0 -1 -1 #> [21,] 0 0 0 -1 0 0 0 4 0 -1 0 #> [22,] -1 0 0 0 -1 -1 -1 0 9 -1 0 #> [23,] 0 0 0 -1 0 -1 0 -1 0 10 -1 #> [24,] 0 -1 0 -1 0 0 0 -1 0 0 7 #> attr(,\"representation\") #> [1] \"laplacian\" #> #> [[3]] #> [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12] [,13] #> [1,] 7 0 -1 -1 0 0 0 0 0 -1 -1 0 0 #> [2,] 0 7 0 -1 -1 -1 -1 0 -1 0 -1 0 0 #> [3,] -1 0 8 -1 0 -1 0 0 0 -1 0 0 0 #> [4,] 0 0 0 10 -1 -1 0 -1 -1 0 0 0 0 #> [5,] -1 -1 0 0 7 -1 0 -1 0 0 0 0 0 #> [6,] 0 -1 0 0 -1 8 -1 0 -1 0 0 0 0 #> [7,] 0 0 0 0 0 -1 3 0 0 0 0 0 0 #> [8,] 0 0 0 0 0 0 0 7 -1 0 -1 0 0 #> [9,] 0 -1 0 0 -1 0 -1 -1 11 -1 -1 0 -1 #> [10,] 0 -1 -1 0 0 0 0 -1 -1 8 0 0 0 #> [11,] 0 0 0 -1 0 -1 0 0 0 0 8 0 -1 #> [12,] -1 0 -1 -1 0 -1 -1 0 0 -1 -1 14 -1 #> [13,] 0 -1 0 -1 -1 0 0 0 0 0 0 0 6 #> [14,] 0 0 0 -1 0 0 0 0 -1 0 -1 0 0 #> [15,] 0 -1 0 0 -1 0 0 -1 0 -1 0 0 -1 #> [16,] -1 0 0 0 0 -1 0 -1 -1 -1 -1 0 0 #> [17,] 0 0 0 0 0 -1 0 0 0 0 0 0 0 #> [18,] 0 0 0 -1 0 -1 0 0 0 0 0 0 0 #> [19,] 0 -1 0 -1 0 0 -1 0 -1 0 0 -1 -1 #> [20,] -1 0 -1 0 -1 0 0 -1 -1 0 0 0 0 #> [21,] -1 0 -1 -1 -1 0 0 0 0 0 -1 0 0 #> [22,] -1 -1 0 0 0 -1 -1 0 0 0 0 -1 -1 #> [23,] 0 -1 -1 0 -1 0 -1 -1 0 0 0 0 0 #> [24,] 0 -1 0 0 0 0 0 0 0 0 -1 0 0 #> [,14] [,15] [,16] [,17] [,18] [,19] [,20] [,21] [,22] [,23] [,24] #> [1,] 0 0 -1 -1 0 0 0 0 0 0 -1 #> [2,] 0 0 0 0 0 0 0 0 -1 0 0 #> [3,] -1 0 0 -1 0 -1 0 0 0 -1 0 #> [4,] -1 -1 -1 -1 -1 -1 0 0 0 0 0 #> [5,] 0 0 0 -1 0 0 0 -1 0 0 -1 #> [6,] 0 0 0 -1 0 -1 -1 0 0 -1 0 #> [7,] 0 0 0 0 0 0 0 -1 0 0 -1 #> [8,] -1 0 -1 0 0 0 -1 0 -1 -1 0 #> [9,] 0 0 -1 0 0 0 -1 -1 0 0 -1 #> [10,] 0 0 0 -1 -1 0 0 0 -1 -1 0 #> [11,] -1 0 0 -1 0 0 -1 -1 0 -1 0 #> [12,] -1 0 0 -1 -1 0 -1 0 -1 0 -1 #> [13,] 0 0 -1 0 -1 0 0 0 0 -1 0 #> [14,] 7 0 -1 0 -1 0 0 0 -1 -1 0 #> [15,] 0 10 0 0 0 -1 -1 0 -1 -1 -1 #> [16,] -1 0 10 0 -1 0 0 0 -1 -1 0 #> [17,] 0 0 0 5 0 0 -1 -1 0 -1 -1 #> [18,] -1 0 0 -1 4 0 0 0 0 0 0 #> [19,] 0 0 0 0 0 7 -1 0 0 0 0 #> [20,] -1 0 0 -1 0 0 9 -1 -1 0 0 #> [21,] -1 -1 0 0 -1 0 -1 11 -1 0 -1 #> [22,] 0 0 0 0 0 0 -1 0 7 0 0 #> [23,] -1 0 0 -1 0 -1 0 0 0 8 0 #> [24,] 0 -1 0 0 0 0 0 0 -1 -1 5 #> attr(,\"representation\") #> [1] \"laplacian\""},{"path":"https://astamm.github.io/nevada/articles/nevada.html","id":"distances-between-networks","dir":"Articles","previous_headings":"","what":"Distances between networks","title":"nevada","text":"possible choose distance consider analysis. Let GG HH two networks NN nodes suppose XX YY matrix representations GG HH, respectively. user can currently choose among 4 distances: Hamming, Frobenius, spectral root-Euclidean. $$ \\rho_H(G,H)=\\frac{1}{N(N-1)}\\sum_{\\neq j}^N \\bigl\\arrowvert X_{,j}-Y_{,j} \\bigr\\arrowvert. $$ nevada, distance can computed dist_hamming(). ρF(G,H)=∥X−Y∥F2=∑≠jN(Xi,j−Yi,j)2. \\rho_F(G,H) = \\left\\| X - Y \\right\\|_F^2 = \\sum_{\\neq j}^N \\bigl ( X_{,j}-Y_{,j} \\bigr )^2. nevada, distance can computed dist_frobenius(). ρS(G,H)=∑≠jN(Λi,jX−Λi,jY)2, \\rho_S(G,H)=\\sum_{\\neq j}^N \\bigl ( \\Lambda^X_{,j}-\\Lambda^Y_{,j} \\bigr )^2, ΛX\\Lambda^X ΛY\\Lambda^Y diagonal matrices eigenvalues diagonal given spectral decomposition matrix representations GG HH. nevada, distance can computed dist_spectral(). ρRE(G,H)=∥X1/2−Y1/2∥F2. \\rho_{RE}(G,H) = \\left\\| X^{1/2} - Y^{1/2} \\right\\|_F^2. Note distance compatible matrix representations requires representation semi-positive definite. nevada, distance can computed dist_root_euclidean(). Pre-computation matrix pairwise distances samples networks alleviates computational burden permutation testing. nevada provides convenient dist_nvd() function exactly object class nvd.","code":"x <- nvd(sample_size = 3L, model = \"gnp\", n = 24L, p = 1/3) #> ℹ Calling the `tidygraph::play_gnp()` function with the following arguments: #> • n: 24 #> • p: 0.333333333333333 #> • directed: TRUE #> • loops: FALSE dist_nvd(x, representation = \"laplacian\", distance = \"hamming\") #> 1 2 #> 2 0.5869565 #> 3 0.5996377 0.5416667"},{"path":"https://astamm.github.io/nevada/articles/nevada.html","id":"hamming-distance","dir":"Articles","previous_headings":"","what":"Hamming distance","title":"nevada","text":"$$ \\rho_H(G,H)=\\frac{1}{N(N-1)}\\sum_{\\neq j}^N \\bigl\\arrowvert X_{,j}-Y_{,j} \\bigr\\arrowvert. $$ nevada, distance can computed dist_hamming().","code":""},{"path":"https://astamm.github.io/nevada/articles/nevada.html","id":"frobenius-distance","dir":"Articles","previous_headings":"","what":"Frobenius distance","title":"nevada","text":"ρF(G,H)=∥X−Y∥F2=∑≠jN(Xi,j−Yi,j)2. \\rho_F(G,H) = \\left\\| X - Y \\right\\|_F^2 = \\sum_{\\neq j}^N \\bigl ( X_{,j}-Y_{,j} \\bigr )^2. nevada, distance can computed dist_frobenius().","code":""},{"path":"https://astamm.github.io/nevada/articles/nevada.html","id":"spectral-distance","dir":"Articles","previous_headings":"","what":"Spectral distance","title":"nevada","text":"ρS(G,H)=∑≠jN(Λi,jX−Λi,jY)2, \\rho_S(G,H)=\\sum_{\\neq j}^N \\bigl ( \\Lambda^X_{,j}-\\Lambda^Y_{,j} \\bigr )^2, ΛX\\Lambda^X ΛY\\Lambda^Y diagonal matrices eigenvalues diagonal given spectral decomposition matrix representations GG HH. nevada, distance can computed dist_spectral().","code":""},{"path":"https://astamm.github.io/nevada/articles/nevada.html","id":"root-euclidean-distance","dir":"Articles","previous_headings":"","what":"Root Euclidean distance","title":"nevada","text":"ρRE(G,H)=∥X1/2−Y1/2∥F2. \\rho_{RE}(G,H) = \\left\\| X^{1/2} - Y^{1/2} \\right\\|_F^2. Note distance compatible matrix representations requires representation semi-positive definite. nevada, distance can computed dist_root_euclidean().","code":""},{"path":"https://astamm.github.io/nevada/articles/nevada.html","id":"computing-a-matrix-of-pairwise-distances-for-an-object-of-class-nvd","dir":"Articles","previous_headings":"","what":"Computing a matrix of pairwise distances for an object of class nvd","title":"nevada","text":"Pre-computation matrix pairwise distances samples networks alleviates computational burden permutation testing. nevada provides convenient dist_nvd() function exactly object class nvd.","code":"x <- nvd(sample_size = 3L, model = \"gnp\", n = 24L, p = 1/3) #> ℹ Calling the `tidygraph::play_gnp()` function with the following arguments: #> • n: 24 #> • p: 0.333333333333333 #> • directed: TRUE #> • loops: FALSE dist_nvd(x, representation = \"laplacian\", distance = \"hamming\") #> 1 2 #> 2 0.5869565 #> 3 0.5996377 0.5416667"},{"path":"https://astamm.github.io/nevada/articles/nevada.html","id":"test-statistics","dir":"Articles","previous_headings":"","what":"Test statistics","title":"nevada","text":"nevada package designed work well flipr package, handles permutation scheme suitable representation, distance test statistics chosen. efficient way two-sample testing network-valued data pertains use statistics based inter-point distances, pairwise distances observations. number test statistics along line proposed literature, including (Lovato et al. 2020). test statistics rely inter-point distances, specific network-valued data. , can found flipr. adopt naming convention test statistic function shall start prefix stat_. statistics based inter-point distances named suffix _ip. list test statistics based inter-point distances currently available flipr: stat_student_ip() alias stat_t_ip() implement Student-like test statistic based inter-point distances proposed Lovato et al. (2020); stat_fisher_ip() alias stat_f_ip() implement Fisher-like test statistic based inter-point distances proposed Lovato et al. (2020); stat_bg_ip() implements statistic proposed Biswas Ghosh (2014); stat_energy_ip() implements class energy-based statistics proposed Székely Rizzo (2013); stat_cq_ip() implements statistic proposed S. X. Chen Qin (2010); stat_mod_ip() implements statistic computes mean inter-point distances; stat_dom_ip() implements statistic computes distance medoids two samples, possibly standardized pooled corresponding variances. also 3 statistics proposed H. Chen, Chen, Su (2018) based similarity graph built top distance matrix: stat_original_edge_count(), stat_generalized_edge_count(), stat_weighted_edge_count(). also Student-like statistics available Frobenius distance can easily compute Fréchet mean. : stat_student_euclidean(), stat_welch_euclidean(). addition test statistic functions already implemented flipr nevada, can also implement function. Test statistic functions compatible flipr least two mandatory input arguments: data either concatenated list size nx+nyn_x + n_y regrouping data points samples distance matrix size (nx+ny)×(nx+ny)(n_x + n_y) \\times (n_x + n_y) stored object class dist. indices1 integer vector size nxn_x storing indices data points belonging first sample current permuted version data. flipr package provides helper function use_stat(nsamples = 2, stat_name = ) makes easy users create test statistic ready used nevada. function creates saves .R file R/ folder current working directory populates following template: instance, flipr-compatible version tt-statistic pooled variance look like: Test statistics passed functions test2_global() test2_local() via argument stats accepts character vector : statistics nevada expected named without stat_ prefix (e.g. \"original_edge_count\" \"student_euclidean\"). statistics flipr expected named without stat_ prefix adding flipr: prefix (e.g., \"flipr:student_ip\"). statistics package pkg expected named without stat_ prefix adding pkg: prefix. Note can also refer test statistic function nevada using naming \"nevada:original_edge_count\" test statistics flipr. mandatory instance yet loaded nevada environment via library(nevada). permutation testing, choice test statistic determines alternative hypothesis, null hypothesis always distributions generated observed samples . means use Student statistic stat_student_ip() instance, actually testing whether means distributions different. ’d rather sensitive differences variances distributions, go Fisher statistic stat_fisher_ip(). can also sensitive multiple aspects distribution testing via permutation framework. achieved hood flipr package implements -called non-parametric combination (NPC) approach proposed Pesarin Salmaso (2010) provide one test statistics stats argument. can read article know implementation flipr. bottom line , example, can choose Student Fisher statistics test simultaneously differences mean variance.","code":"#' Test Statistic for the Two-Sample Problem #' #' This function computes the test statistic... #' #' @param data A list storing the concatenation of the two samples from which #' the user wants to make inference. Alternatively, a distance matrix stored #' in an object of class \\code{\\link[stats]{dist}} of pairwise distances #' between data points. #' @param indices1 An integer vector that contains the indices of the data #' points belong to the first sample in the current permuted version of the #' data. #' #' @return A numeric value evaluating the desired test statistic. #' @export #' #' @examples #' # TO BE DONE BY THE DEVELOPER OF THE PACKAGE stat_{{{name}}} <- function(data, indices1) { n <- if (inherits(data, \"dist\")) attr(data, \"Size\") else if (inherits(data, \"list\")) length(data) else stop(\"The `data` input should be of class either list or dist.\") indices2 <- seq_len(n)[-indices1] x <- data[indices1] y <- data[indices2] # Here comes the code that computes the desired test # statistic from input samples stored in lists x and y } stat_student <- function(data, indices1) { n <- if (inherits(data, \"dist\")) attr(data, \"Size\") else if (inherits(data, \"list\")) length(data) else stop(\"The `data` input should be of class either list or dist.\") indices2 <- seq_len(n)[-indices1] x <- data[indices1] y <- data[indices2] # Here comes the code that computes the desired test # statistic from input samples stored in lists x and y x <- unlist(x) y <- unlist(y) stats::t.test(x, y, var.equal = TRUE)$statistic } x <- nvd(sample_size = 10L, model = \"gnp\", n = 24L, p = 1/3) #> ℹ Calling the `tidygraph::play_gnp()` function with the following arguments: #> • n: 24 #> • p: 0.333333333333333 #> • directed: TRUE #> • loops: FALSE y <- nvd(sample_size = 10L, model = \"degree\" , out_degree = rep(2, 24L), method = \"configuration\") #> ℹ Calling the `tidygraph::play_degree()` function with the following arguments: #> • out_degree: 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, …, 2, and 2 #> • method: configuration #> • in_degree: NULL test2_global( x = x, y = y, representation = \"laplacian\", distance = \"frobenius\", stats = c(\"flipr:student_ip\", \"flipr:fisher_ip\"), seed = 1234 )$pvalue #> [1] 0.0009962984"},{"path":"https://astamm.github.io/nevada/articles/nevada.html","id":"available-statistics","dir":"Articles","previous_headings":"","what":"Available statistics","title":"nevada","text":"number test statistics along line proposed literature, including (Lovato et al. 2020). test statistics rely inter-point distances, specific network-valued data. , can found flipr. adopt naming convention test statistic function shall start prefix stat_. statistics based inter-point distances named suffix _ip. list test statistics based inter-point distances currently available flipr: stat_student_ip() alias stat_t_ip() implement Student-like test statistic based inter-point distances proposed Lovato et al. (2020); stat_fisher_ip() alias stat_f_ip() implement Fisher-like test statistic based inter-point distances proposed Lovato et al. (2020); stat_bg_ip() implements statistic proposed Biswas Ghosh (2014); stat_energy_ip() implements class energy-based statistics proposed Székely Rizzo (2013); stat_cq_ip() implements statistic proposed S. X. Chen Qin (2010); stat_mod_ip() implements statistic computes mean inter-point distances; stat_dom_ip() implements statistic computes distance medoids two samples, possibly standardized pooled corresponding variances. also 3 statistics proposed H. Chen, Chen, Su (2018) based similarity graph built top distance matrix: stat_original_edge_count(), stat_generalized_edge_count(), stat_weighted_edge_count(). also Student-like statistics available Frobenius distance can easily compute Fréchet mean. : stat_student_euclidean(), stat_welch_euclidean(). addition test statistic functions already implemented flipr nevada, can also implement function. Test statistic functions compatible flipr least two mandatory input arguments: data either concatenated list size nx+nyn_x + n_y regrouping data points samples distance matrix size (nx+ny)×(nx+ny)(n_x + n_y) \\times (n_x + n_y) stored object class dist. indices1 integer vector size nxn_x storing indices data points belonging first sample current permuted version data. flipr package provides helper function use_stat(nsamples = 2, stat_name = ) makes easy users create test statistic ready used nevada. function creates saves .R file R/ folder current working directory populates following template: instance, flipr-compatible version tt-statistic pooled variance look like:","code":"#' Test Statistic for the Two-Sample Problem #' #' This function computes the test statistic... #' #' @param data A list storing the concatenation of the two samples from which #' the user wants to make inference. Alternatively, a distance matrix stored #' in an object of class \\code{\\link[stats]{dist}} of pairwise distances #' between data points. #' @param indices1 An integer vector that contains the indices of the data #' points belong to the first sample in the current permuted version of the #' data. #' #' @return A numeric value evaluating the desired test statistic. #' @export #' #' @examples #' # TO BE DONE BY THE DEVELOPER OF THE PACKAGE stat_{{{name}}} <- function(data, indices1) { n <- if (inherits(data, \"dist\")) attr(data, \"Size\") else if (inherits(data, \"list\")) length(data) else stop(\"The `data` input should be of class either list or dist.\") indices2 <- seq_len(n)[-indices1] x <- data[indices1] y <- data[indices2] # Here comes the code that computes the desired test # statistic from input samples stored in lists x and y } stat_student <- function(data, indices1) { n <- if (inherits(data, \"dist\")) attr(data, \"Size\") else if (inherits(data, \"list\")) length(data) else stop(\"The `data` input should be of class either list or dist.\") indices2 <- seq_len(n)[-indices1] x <- data[indices1] y <- data[indices2] # Here comes the code that computes the desired test # statistic from input samples stored in lists x and y x <- unlist(x) y <- unlist(y) stats::t.test(x, y, var.equal = TRUE)$statistic }"},{"path":"https://astamm.github.io/nevada/articles/nevada.html","id":"from-flipr","dir":"Articles","previous_headings":"Test statistics","what":"From flipr","title":"nevada","text":"number test statistics along line proposed literature, including (Lovato et al. 2020). test statistics rely inter-point distances, specific network-valued data. , can found flipr. adopt naming convention test statistic function shall start prefix stat_. statistics based inter-point distances named suffix _ip. list test statistics based inter-point distances currently available flipr: stat_student_ip() alias stat_t_ip() implement Student-like test statistic based inter-point distances proposed Lovato et al. (2020); stat_fisher_ip() alias stat_f_ip() implement Fisher-like test statistic based inter-point distances proposed Lovato et al. (2020); stat_bg_ip() implements statistic proposed Biswas Ghosh (2014); stat_energy_ip() implements class energy-based statistics proposed Székely Rizzo (2013); stat_cq_ip() implements statistic proposed S. X. Chen Qin (2010); stat_mod_ip() implements statistic computes mean inter-point distances; stat_dom_ip() implements statistic computes distance medoids two samples, possibly standardized pooled corresponding variances.","code":""},{"path":"https://astamm.github.io/nevada/articles/nevada.html","id":"from-nevada","dir":"Articles","previous_headings":"Test statistics","what":"From nevada","title":"nevada","text":"also 3 statistics proposed H. Chen, Chen, Su (2018) based similarity graph built top distance matrix: stat_original_edge_count(), stat_generalized_edge_count(), stat_weighted_edge_count(). also Student-like statistics available Frobenius distance can easily compute Fréchet mean. : stat_student_euclidean(), stat_welch_euclidean().","code":""},{"path":"https://astamm.github.io/nevada/articles/nevada.html","id":"write-your-own-test-statistic-function","dir":"Articles","previous_headings":"Test statistics","what":"Write your own test statistic function","title":"nevada","text":"addition test statistic functions already implemented flipr nevada, can also implement function. Test statistic functions compatible flipr least two mandatory input arguments: data either concatenated list size nx+nyn_x + n_y regrouping data points samples distance matrix size (nx+ny)×(nx+ny)(n_x + n_y) \\times (n_x + n_y) stored object class dist. indices1 integer vector size nxn_x storing indices data points belonging first sample current permuted version data. flipr package provides helper function use_stat(nsamples = 2, stat_name = ) makes easy users create test statistic ready used nevada. function creates saves .R file R/ folder current working directory populates following template: instance, flipr-compatible version tt-statistic pooled variance look like:","code":"#' Test Statistic for the Two-Sample Problem #' #' This function computes the test statistic... #' #' @param data A list storing the concatenation of the two samples from which #' the user wants to make inference. Alternatively, a distance matrix stored #' in an object of class \\code{\\link[stats]{dist}} of pairwise distances #' between data points. #' @param indices1 An integer vector that contains the indices of the data #' points belong to the first sample in the current permuted version of the #' data. #' #' @return A numeric value evaluating the desired test statistic. #' @export #' #' @examples #' # TO BE DONE BY THE DEVELOPER OF THE PACKAGE stat_{{{name}}} <- function(data, indices1) { n <- if (inherits(data, \"dist\")) attr(data, \"Size\") else if (inherits(data, \"list\")) length(data) else stop(\"The `data` input should be of class either list or dist.\") indices2 <- seq_len(n)[-indices1] x <- data[indices1] y <- data[indices2] # Here comes the code that computes the desired test # statistic from input samples stored in lists x and y } stat_student <- function(data, indices1) { n <- if (inherits(data, \"dist\")) attr(data, \"Size\") else if (inherits(data, \"list\")) length(data) else stop(\"The `data` input should be of class either list or dist.\") indices2 <- seq_len(n)[-indices1] x <- data[indices1] y <- data[indices2] # Here comes the code that computes the desired test # statistic from input samples stored in lists x and y x <- unlist(x) y <- unlist(y) stats::t.test(x, y, var.equal = TRUE)$statistic }"},{"path":"https://astamm.github.io/nevada/articles/nevada.html","id":"usage","dir":"Articles","previous_headings":"","what":"Usage","title":"nevada","text":"Test statistics passed functions test2_global() test2_local() via argument stats accepts character vector : statistics nevada expected named without stat_ prefix (e.g. \"original_edge_count\" \"student_euclidean\"). statistics flipr expected named without stat_ prefix adding flipr: prefix (e.g., \"flipr:student_ip\"). statistics package pkg expected named without stat_ prefix adding pkg: prefix. Note can also refer test statistic function nevada using naming \"nevada:original_edge_count\" test statistics flipr. mandatory instance yet loaded nevada environment via library(nevada). permutation testing, choice test statistic determines alternative hypothesis, null hypothesis always distributions generated observed samples . means use Student statistic stat_student_ip() instance, actually testing whether means distributions different. ’d rather sensitive differences variances distributions, go Fisher statistic stat_fisher_ip(). can also sensitive multiple aspects distribution testing via permutation framework. achieved hood flipr package implements -called non-parametric combination (NPC) approach proposed Pesarin Salmaso (2010) provide one test statistics stats argument. can read article know implementation flipr. bottom line , example, can choose Student Fisher statistics test simultaneously differences mean variance.","code":"x <- nvd(sample_size = 10L, model = \"gnp\", n = 24L, p = 1/3) #> ℹ Calling the `tidygraph::play_gnp()` function with the following arguments: #> • n: 24 #> • p: 0.333333333333333 #> • directed: TRUE #> • loops: FALSE y <- nvd(sample_size = 10L, model = \"degree\" , out_degree = rep(2, 24L), method = \"configuration\") #> ℹ Calling the `tidygraph::play_degree()` function with the following arguments: #> • out_degree: 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, …, 2, and 2 #> • method: configuration #> • in_degree: NULL test2_global( x = x, y = y, representation = \"laplacian\", distance = \"frobenius\", stats = c(\"flipr:student_ip\", \"flipr:fisher_ip\"), seed = 1234 )$pvalue #> [1] 0.0009962984"},{"path":"https://astamm.github.io/nevada/articles/nevada.html","id":"naming-conventions","dir":"Articles","previous_headings":"Test statistics","what":"Naming conventions","title":"nevada","text":"Test statistics passed functions test2_global() test2_local() via argument stats accepts character vector : statistics nevada expected named without stat_ prefix (e.g. \"original_edge_count\" \"student_euclidean\"). statistics flipr expected named without stat_ prefix adding flipr: prefix (e.g., \"flipr:student_ip\"). statistics package pkg expected named without stat_ prefix adding pkg: prefix. Note can also refer test statistic function nevada using naming \"nevada:original_edge_count\" test statistics flipr. mandatory instance yet loaded nevada environment via library(nevada).","code":"x <- nvd(sample_size = 10L, model = \"gnp\", n = 24L, p = 1/3) #> ℹ Calling the `tidygraph::play_gnp()` function with the following arguments: #> • n: 24 #> • p: 0.333333333333333 #> • directed: TRUE #> • loops: FALSE y <- nvd(sample_size = 10L, model = \"degree\" , out_degree = rep(2, 24L), method = \"configuration\") #> ℹ Calling the `tidygraph::play_degree()` function with the following arguments: #> • out_degree: 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, …, 2, and 2 #> • method: configuration #> • in_degree: NULL test2_global( x = x, y = y, representation = \"laplacian\", distance = \"frobenius\", stats = c(\"flipr:student_ip\", \"flipr:fisher_ip\"), seed = 1234 )$pvalue #> [1] 0.0009962984"},{"path":"https://astamm.github.io/nevada/articles/nevada.html","id":"using-multiple-test-statistics","dir":"Articles","previous_headings":"Test statistics","what":"Using multiple test statistics","title":"nevada","text":"permutation testing, choice test statistic determines alternative hypothesis, null hypothesis always distributions generated observed samples . means use Student statistic stat_student_ip() instance, actually testing whether means distributions different. ’d rather sensitive differences variances distributions, go Fisher statistic stat_fisher_ip(). can also sensitive multiple aspects distribution testing via permutation framework. achieved hood flipr package implements -called non-parametric combination (NPC) approach proposed Pesarin Salmaso (2010) provide one test statistics stats argument. can read article know implementation flipr. bottom line , example, can choose Student Fisher statistics test simultaneously differences mean variance.","code":""},{"path":[]},{"path":"https://astamm.github.io/nevada/authors.html","id":null,"dir":"","previous_headings":"","what":"Authors","title":"Authors and Citation","text":"Ilenia Lovato. Author. Alessia Pini. Author. Aymeric Stamm. Author, maintainer. Simone Vantini. Author.","code":""},{"path":"https://astamm.github.io/nevada/authors.html","id":"citation","dir":"","previous_headings":"","what":"Citation","title":"Authors and Citation","text":"Lovato , Pini , Stamm , Vantini S (2024). nevada: Network-Valued Data Analysis. R package version 0.2.0.9000, https://github.com/astamm/nevada/, https://astamm.github.io/nevada/.","code":"@Manual{, title = {nevada: Network-Valued Data Analysis}, author = {Ilenia Lovato and Alessia Pini and Aymeric Stamm and Simone Vantini}, year = {2024}, note = {R package version 0.2.0.9000, https://github.com/astamm/nevada/}, url = {https://astamm.github.io/nevada/}, }"},{"path":"https://astamm.github.io/nevada/index.html","id":"overview-","dir":"","previous_headings":"","what":"Network-Valued Data Analysis","title":"Network-Valued Data Analysis","text":"package nevada (NEtwork-VAlued Data Analysis) R package statistical analysis network-valued data. setting, sample made statistical units networks . package provides set matrix representations networks network-valued data can transformed matrix-valued data. Subsequently, number distances matrices provided well quantify far two networks several test statistics proposed testing equality distribution samples networks using exact permutation testing procedures. permutation scheme carried flipr package also provides number test statistics based inter-point distances play nicely network-valued data. implementation largely made C++ matrix inter- intra-sample distances pre-computed, alleviates computational burden often associated permutation tests.","code":""},{"path":"https://astamm.github.io/nevada/index.html","id":"installation","dir":"","previous_headings":"","what":"Installation","title":"Network-Valued Data Analysis","text":"can install latest stable version nevada CRAN : can install development version GitHub :","code":"install.packages(\"nevada\") # install.packages(\"remotes\") remotes::install_github(\"astamm/nevada\")"},{"path":[]},{"path":"https://astamm.github.io/nevada/index.html","id":"example-1","dir":"","previous_headings":"Usage","what":"Example 1","title":"Network-Valued Data Analysis","text":"first example, compare two populations networks generated according two different models (Watts-Strogatz Barabasi), using adjacency matrix representation networks, Frobenius distance compare single networks combination Student-like Fisher-like statistics based inter-point distances summarize information perform permutation test. default nvd() constructor generates networks 25 nodes. One can wonder whether difference distributions generated two samples (given models used). test2_global() function provides answer question: p-value small, leading conclusion reject null hypothesis equal distributions. Although fake example, create partition try localize differences along partition: test2_local() function provides answer question:","code":"sample_size <- 10L num_vertices <- 10L smallworld_params <- list(n_dim = 1L, dim_size = num_vertices, order = 4L, p_rewire = 0.15) barabasi_albert_params <- list(power = 1L, n = num_vertices) withr::with_seed(1234, { x <- nevada::nvd( sample_size = sample_size, model = \"smallworld\", !!!smallworld_params ) y <- nevada::nvd( sample_size = sample_size, model = \"barabasi_albert\", !!!barabasi_albert_params ) }) ℹ Calling the `tidygraph::play_smallworld()` function with the following arguments: • n_dim: 1 • dim_size: 10 • order: 4 • p_rewire: 0.15 • loops: FALSE • multiple: FALSE ℹ Calling the `tidygraph::play_barabasi_albert()` function with the following arguments: • power: 1 • n: 10 • growth: 1 • growth_dist: NULL • use_out: FALSE • appeal_zero: 1 • directed: TRUE • method: psumtree t1_global <- nevada::test2_global(x, y, seed = 1234) t1_global$pvalue [1] 0.0009962984 partition <- as.integer(c(1:5, each = 5)) t1_local <- nevada::test2_local(x, y, partition, seed = 1234) t1_local $intra # A tibble: 5 × 3 E pvalue truncated 1 P1 0.425 TRUE 2 P2 0.425 TRUE 3 P3 0.425 TRUE 4 P4 0.425 TRUE 5 P5 0.425 TRUE $inter # A tibble: 10 × 4 E1 E2 pvalue truncated 1 P1 P2 0.000996 FALSE 2 P1 P3 0.000996 FALSE 3 P1 P4 0.000996 FALSE 4 P1 P5 0.000996 FALSE 5 P2 P3 0.000996 FALSE 6 P2 P4 0.000996 FALSE 7 P2 P5 0.000996 FALSE 8 P3 P4 0.000996 FALSE 9 P3 P5 0.000996 FALSE 10 P4 P5 0.000996 FALSE"},{"path":"https://astamm.github.io/nevada/index.html","id":"example-2","dir":"","previous_headings":"Usage","what":"Example 2","title":"Network-Valued Data Analysis","text":"second example, compare two populations networks generated according model (Watts-Strogatz), using adjacency matrix representation networks, Frobenius distance compare single networks combination Student-like Fisher-like statistics based inter-point distances summarize information perform permutation test. One can wonder whether difference distributions generated two samples (given models used). test2_global() function provides answer question: p-value larger 5% even 10%, leading us failing reject null hypothesis equal distributions significance thresholds.","code":"withr::with_seed(1234, { x <- nevada::nvd( sample_size = sample_size, model = \"smallworld\", !!!smallworld_params ) y <- nevada::nvd( sample_size = sample_size, model = \"smallworld\", !!!smallworld_params ) }) ℹ Calling the `tidygraph::play_smallworld()` function with the following arguments: • n_dim: 1 • dim_size: 10 • order: 4 • p_rewire: 0.15 • loops: FALSE • multiple: FALSE ℹ Calling the `tidygraph::play_smallworld()` function with the following arguments: • n_dim: 1 • dim_size: 10 • order: 4 • p_rewire: 0.15 • loops: FALSE • multiple: FALSE t2 <- nevada::test2_global(x, y, seed = 1234) t2$pvalue [1] 0.9190782"},{"path":"https://astamm.github.io/nevada/reference/as_nvd.html","id":null,"dir":"Reference","previous_headings":"","what":"Coercion to Network-Valued Data Object — as_nvd","title":"Coercion to Network-Valued Data Object — as_nvd","text":"function flags list igraph objects nvd object defined package.","code":""},{"path":"https://astamm.github.io/nevada/reference/as_nvd.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Coercion to Network-Valued Data Object — as_nvd","text":"","code":"as_nvd(obj)"},{"path":"https://astamm.github.io/nevada/reference/as_nvd.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Coercion to Network-Valued Data Object — as_nvd","text":"obj list igraph objects.","code":""},{"path":"https://astamm.github.io/nevada/reference/as_nvd.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Coercion to Network-Valued Data Object — as_nvd","text":"nvd object.","code":""},{"path":"https://astamm.github.io/nevada/reference/as_nvd.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Coercion to Network-Valued Data Object — as_nvd","text":"","code":"params <- list(n_dim = 1L, dim_size = 4L, order = 4L, p_rewire = 0.15) out <- nvd(sample_size = 1L, model = \"smallworld\", !!!params) #> ℹ Calling the `tidygraph::play_smallworld()` function with the following arguments: #> • n_dim: 1 #> • dim_size: 4 #> • order: 4 #> • p_rewire: 0.15 #> • loops: FALSE #> • multiple: FALSE as_nvd(out) #> [[1]] #> # A tbl_graph: 4 nodes and 6 edges #> # #> # An undirected simple graph with 1 component #> # #> # Node Data: 4 × 0 (active) #> # #> # Edge Data: 6 × 2 #> from to #> #> 1 1 2 #> 2 2 3 #> 3 3 4 #> # ℹ 3 more rows #> #> attr(,\"class\") #> [1] \"nvd\" \"list\""},{"path":"https://astamm.github.io/nevada/reference/as_vertex_partition.html","id":null,"dir":"Reference","previous_headings":"","what":"Coercion to Vertex Partition — as_vertex_partition","title":"Coercion to Vertex Partition — as_vertex_partition","text":"function converts vector memberships proper vertex partition object.","code":""},{"path":"https://astamm.github.io/nevada/reference/as_vertex_partition.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Coercion to Vertex Partition — as_vertex_partition","text":"","code":"as_vertex_partition(x)"},{"path":"https://astamm.github.io/nevada/reference/as_vertex_partition.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Coercion to Vertex Partition — as_vertex_partition","text":"x list grouping vertices partition element integer character vector vertex memberships.","code":""},{"path":"https://astamm.github.io/nevada/reference/as_vertex_partition.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Coercion to Vertex Partition — as_vertex_partition","text":"vertex_partition object storing corresponding vertex partition.","code":""},{"path":"https://astamm.github.io/nevada/reference/as_vertex_partition.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Coercion to Vertex Partition — as_vertex_partition","text":"","code":"m1 <- c(\"P1\", \"P3\", \"P4\", \"P1\", \"P2\", \"P2\", \"P3\", \"P1\", \"P4\", \"P3\") V1 <- as_vertex_partition(m1) m2 <- as.integer(c(1, 3, 4, 1, 2, 2, 3, 1, 4, 3)) V2 <- as_vertex_partition(m2)"},{"path":"https://astamm.github.io/nevada/reference/dist_nvd.html","id":null,"dir":"Reference","previous_headings":"","what":"Pairwise Distance Matrix Between Two Samples of Networks — dist_nvd","title":"Pairwise Distance Matrix Between Two Samples of Networks — dist_nvd","text":"function computes matrix pairwise distances elements two samples put together. cardinality fist sample denoted \\(n_1\\) second one denoted \\(n_2\\).","code":""},{"path":"https://astamm.github.io/nevada/reference/dist_nvd.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Pairwise Distance Matrix Between Two Samples of Networks — dist_nvd","text":"","code":"dist_nvd( x, y = NULL, representation = \"adjacency\", distance = \"frobenius\", matching_iterations = 0, target_matrix = NULL )"},{"path":"https://astamm.github.io/nevada/reference/dist_nvd.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Pairwise Distance Matrix Between Two Samples of Networks — dist_nvd","text":"x base::list tidygraph::tbl_graph objects matrix representations underlying networks given first population. y base::list tidygraph::tbl_graph objects matrix representations underlying networks given second population. representation string specifying desired type representation, among: \"adjacency\", \"laplacian\", \"modularity\" \"graphon\". Default \"laplacian\". distance string specifying chosen distance calculating test statistic, among: \"hamming\", \"frobenius\", \"spectral\" \"root-euclidean\". Default \"frobenius\". matching_iterations integer value specifying maximum number runs looking optimal permutation graph matching. Defaults 0L case matching done. target_matrix square numeric matrix size n equal order graphs specifying target matrix towards initial doubly stochastic matrix shrunk time graph matching algorithm fails provide good minimum. Defaults NULL case target matrix automatically chosen identity matrix uniform matrix n-simplex.","code":""},{"path":"https://astamm.github.io/nevada/reference/dist_nvd.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Pairwise Distance Matrix Between Two Samples of Networks — dist_nvd","text":"matrix dimension \\((n_1+n_2) \\times (n_1+n_2)\\) containing distances elements two samples put together.","code":""},{"path":"https://astamm.github.io/nevada/reference/dist_nvd.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Pairwise Distance Matrix Between Two Samples of Networks — dist_nvd","text":"","code":"gnp_params <- list(n = 24L, p = 1/3) degree_params <- list(out_degree = rep(2, 24L), method = \"configuration\") x <- nvd(sample_size = 10L, model = \"gnp\", !!!gnp_params) #> ℹ Calling the `tidygraph::play_gnp()` function with the following arguments: #> • n: 24 #> • p: 0.333333333333333 #> • directed: TRUE #> • loops: FALSE y <- nvd(sample_size = 10L, model = \"degree\", !!!degree_params) #> ℹ Calling the `tidygraph::play_degree()` function with the following arguments: #> • out_degree: 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, …, 2, and 2 #> • method: configuration #> • in_degree: NULL dist_nvd(x, y, \"adjacency\", \"spectral\") #> 1 2 3 4 5 6 7 #> 2 1.3247846 #> 3 1.0327248 0.9033180 #> 4 1.5853265 1.6640296 1.7191641 #> 5 0.9666449 1.4355136 1.2589486 1.3497579 #> 6 1.8110275 1.5013356 1.8511752 1.2436566 1.4344913 #> 7 1.3930286 1.4059886 1.5364497 1.1343736 1.0990257 0.9076238 #> 8 1.2303792 1.5106096 1.4119224 1.6730651 1.3688597 1.6864406 1.2009165 #> 9 1.1101856 1.2287318 1.3380202 1.5881906 0.9484409 1.3067718 0.9976968 #> 10 2.1893772 2.0652489 2.3058835 1.4329811 2.1422303 1.4517239 1.5917795 #> 11 8.4867947 8.5608153 8.7547574 7.4780207 8.2803750 7.4567586 7.7232314 #> 12 8.4422768 8.5215249 8.7216879 7.4711314 8.2429917 7.4256876 7.7030848 #> 13 8.3326960 8.4244411 8.6346130 7.2954696 8.0754004 7.2667769 7.5421763 #> 14 8.5346271 8.6472123 8.8305416 7.5621490 8.3493604 7.5456648 7.7836831 #> 15 8.4507363 8.5152352 8.7053939 7.4405549 8.2445197 7.4250752 7.6844996 #> 16 8.5612955 8.6429671 8.8154116 7.6008036 8.3980884 7.5923383 7.8293452 #> 17 8.7016700 8.7882495 8.9736385 7.7333608 8.5226313 7.6957167 7.9396531 #> 18 8.5984466 8.6848386 8.8748586 7.6466974 8.4189707 7.6032316 7.8775459 #> 19 8.5142376 8.6069190 8.7932205 7.5435473 8.3396354 7.5338812 7.7876685 #> 20 8.7145670 8.8895109 9.0224292 7.8085073 8.5666788 7.8687106 8.0494336 #> 8 9 10 11 12 13 14 #> 2 #> 3 #> 4 #> 5 #> 6 #> 7 #> 8 #> 9 1.1048100 #> 10 2.0321761 2.1846303 #> 11 8.3134499 8.4229044 6.6444501 #> 12 8.2746230 8.3994799 6.6304228 0.7369126 #> 13 8.1406785 8.2364872 6.5535510 1.2683823 1.3336147 #> 14 8.3549279 8.4946292 6.7359199 0.9783101 1.1464892 1.0788921 #> 15 8.2628771 8.3869980 6.6250181 0.7239710 0.6074279 1.3083881 1.1218164 #> 16 8.3952254 8.5488617 6.7202718 0.6934316 0.8810910 1.6705284 1.0485169 #> 17 8.5071303 8.6499853 6.8451125 1.1513150 1.5204346 1.6132610 1.0345899 #> 18 8.4544076 8.5696768 6.7655138 0.5638243 0.7853323 1.5476022 1.0788974 #> 19 8.3476217 8.4767803 6.6939736 0.5954485 0.6107754 1.4131486 0.9632040 #> 20 8.5461863 8.7305567 7.0410593 2.0052855 2.0542314 2.0288872 1.6862530 #> 15 16 17 18 19 #> 2 #> 3 #> 4 #> 5 #> 6 #> 7 #> 8 #> 9 #> 10 #> 11 #> 12 #> 13 #> 14 #> 15 #> 16 0.9222237 #> 17 1.5016252 1.1529340 #> 18 0.9899725 0.6758305 1.1875108 #> 19 0.5506270 0.7299532 1.3193354 0.6945410 #> 20 1.9859817 2.0844278 2.3432337 1.9666672 1.8500806"},{"path":"https://astamm.github.io/nevada/reference/distances.html","id":null,"dir":"Reference","previous_headings":"","what":"Distances Between Networks — distances","title":"Distances Between Networks — distances","text":"collection functions computing distance two networks.","code":""},{"path":"https://astamm.github.io/nevada/reference/distances.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Distances Between Networks — distances","text":"","code":"dist_hamming(x, y, representation = \"laplacian\") dist_frobenius( x, y, representation = \"laplacian\", matching_iterations = 0, target_matrix = NULL ) dist_spectral(x, y, representation = \"laplacian\") dist_root_euclidean(x, y, representation = \"laplacian\")"},{"path":"https://astamm.github.io/nevada/reference/distances.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Distances Between Networks — distances","text":"x tidygraph::tbl_graph object matrix representing underlying network. y tidygraph::tbl_graph object matrix representing underlying network. number vertices x. representation string specifying desired type representation, among: \"adjacency\", \"laplacian\", \"modularity\" \"graphon\". Default \"laplacian\". matching_iterations integer value specifying maximum number runs looking optimal permutation graph matching. Defaults 0L case matching done. target_matrix square numeric matrix size n equal order graphs specifying target matrix towards initial doubly stochastic matrix shrunk time graph matching algorithm fails provide good minimum. Defaults NULL case target matrix automatically chosen identity matrix uniform matrix n-simplex.","code":""},{"path":"https://astamm.github.io/nevada/reference/distances.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Distances Between Networks — distances","text":"scalar measuring distance two input networks.","code":""},{"path":"https://astamm.github.io/nevada/reference/distances.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Distances Between Networks — distances","text":"Let \\(X\\) matrix representation network \\(x\\) \\(Y\\) matrix representation network \\(y\\). Hamming distance \\(x\\) \\(y\\) given $$\\frac{1}{N(N-1)} \\sum_{,j} |X_{ij} - Y_{ij}|,$$ \\(N\\) number vertices networks \\(x\\) \\(y\\). Frobenius distance \\(x\\) \\(y\\) given $$\\sqrt{\\sum_{,j} (X_{ij} - Y_{ij})^2}.$$ spectral distance \\(x\\) \\(y\\) given $$\\sqrt{\\sum_i (a_i - b_i)^2},$$ \\(\\) \\(b\\) eigenvalues \\(X\\) \\(Y\\), respectively. distance gives rise classes equivalence. Consider spectral decomposition \\(X\\) \\(Y\\): $$X=VAV^{-1}$$ $$Y = UBU^{-1},$$ \\(V\\) \\(U\\) matrices whose columns eigenvectors \\(X\\) \\(Y\\), respectively \\(\\) \\(B\\) diagonal matrices elements eigenvalues \\(X\\) \\(Y\\), respectively. root-Euclidean distance \\(x\\) \\(y\\) given $$\\sqrt{\\sum_i (V \\sqrt{} V^{-1} - U \\sqrt{B} U^{-1})^2}.$$ Root-Euclidean distance can used laplacian matrix representation.","code":""},{"path":"https://astamm.github.io/nevada/reference/distances.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Distances Between Networks — distances","text":"","code":"g1 <- igraph::sample_gnp(20, 0.1) g2 <- igraph::sample_gnp(20, 0.2) dist_hamming(g1, g2, \"adjacency\") #> [1] 0.2526316 dist_frobenius(g1, g2, \"adjacency\") #> [1] 9.797959 dist_spectral(g1, g2, \"laplacian\") #> [1] 12.74562 dist_root_euclidean(g1, g2, \"laplacian\") #> [1] 10.22699"},{"path":"https://astamm.github.io/nevada/reference/edge_count_global_variables.html","id":null,"dir":"Reference","previous_headings":"","what":"Transform distance matrix in edge properties of minimal spanning tree — edge_count_global_variables","title":"Transform distance matrix in edge properties of minimal spanning tree — edge_count_global_variables","text":"Transform distance matrix edge properties minimal spanning tree","code":""},{"path":"https://astamm.github.io/nevada/reference/edge_count_global_variables.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Transform distance matrix in edge properties of minimal spanning tree — edge_count_global_variables","text":"","code":"edge_count_global_variables(d, n1, k = 1L)"},{"path":"https://astamm.github.io/nevada/reference/edge_count_global_variables.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Transform distance matrix in edge properties of minimal spanning tree — edge_count_global_variables","text":"d matrix dimension \\((n1+n2)x(n1+n2)\\) containing distances elements two samples put together. n1 integer giving size first sample. k integer specifying density minimal spanning tree generate.","code":""},{"path":"https://astamm.github.io/nevada/reference/edge_count_global_variables.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Transform distance matrix in edge properties of minimal spanning tree — edge_count_global_variables","text":"list edge properties minimal spanning tree.","code":""},{"path":"https://astamm.github.io/nevada/reference/edge_count_global_variables.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Transform distance matrix in edge properties of minimal spanning tree — edge_count_global_variables","text":"","code":"n1 <- 30L n2 <- 10L gnp_params <- list(n = 24L, p = 1/3) degree_params <- list(out_degree = rep(2, 24L), method = \"configuration\") x <- nvd(sample_size = n1, model = \"gnp\", !!!gnp_params) #> ℹ Calling the `tidygraph::play_gnp()` function with the following arguments: #> • n: 24 #> • p: 0.333333333333333 #> • directed: TRUE #> • loops: FALSE y <- nvd(sample_size = n2, model = \"degree\", !!!degree_params) #> ℹ Calling the `tidygraph::play_degree()` function with the following arguments: #> • out_degree: 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, …, 2, and 2 #> • method: configuration #> • in_degree: NULL d <- dist_nvd(x, y, representation = \"laplacian\", distance = \"frobenius\") e <- edge_count_global_variables(d, n1, k = 5L)"},{"path":"https://astamm.github.io/nevada/reference/generate_sigma_algebra.html","id":null,"dir":"Reference","previous_headings":"","what":"Sigma-Algebra generated by a Partition — generate_sigma_algebra","title":"Sigma-Algebra generated by a Partition — generate_sigma_algebra","text":"Sigma-Algebra generated Partition","code":""},{"path":"https://astamm.github.io/nevada/reference/generate_sigma_algebra.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Sigma-Algebra generated by a Partition — generate_sigma_algebra","text":"","code":"generate_sigma_algebra(x)"},{"path":"https://astamm.github.io/nevada/reference/generate_sigma_algebra.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Sigma-Algebra generated by a Partition — generate_sigma_algebra","text":"x Input partition stored vertex_partition object.","code":""},{"path":"https://astamm.github.io/nevada/reference/generate_sigma_algebra.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Sigma-Algebra generated by a Partition — generate_sigma_algebra","text":"Sigma-algebra","code":""},{"path":"https://astamm.github.io/nevada/reference/generate_sigma_algebra.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Sigma-Algebra generated by a Partition — generate_sigma_algebra","text":"","code":"g <- igraph::make_ring(7) m <- as.integer(c(1, 2, 1, 3, 4, 4, 3)) p <- as_vertex_partition(m) sa <- generate_sigma_algebra(p) all_full <- purrr::modify_depth(sa, 2, ~ subgraph_full (g, .x)) all_intra <- purrr::modify_depth(sa, 2, ~ subgraph_intra(g, .x)) all_inter <- purrr::modify_depth(sa, 2, ~ subgraph_inter(g, .x))"},{"path":"https://astamm.github.io/nevada/reference/inner-products.html","id":null,"dir":"Reference","previous_headings":"","what":"Inner-Products Between Networks — inner-products","title":"Inner-Products Between Networks — inner-products","text":"collection functions computing inner product two networks.","code":""},{"path":"https://astamm.github.io/nevada/reference/inner-products.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Inner-Products Between Networks — inner-products","text":"","code":"ipro_frobenius(x, y, representation = \"laplacian\")"},{"path":"https://astamm.github.io/nevada/reference/inner-products.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Inner-Products Between Networks — inner-products","text":"x igraph object matrix representing underlying network. y igraph object matrix representing underlying network. number vertices x. representation string specifying desired type representation, among: \"adjacency\", \"laplacian\", \"modularity\" \"graphon\". Default \"laplacian\".","code":""},{"path":"https://astamm.github.io/nevada/reference/inner-products.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Inner-Products Between Networks — inner-products","text":"scalar measuring angle two input networks.","code":""},{"path":"https://astamm.github.io/nevada/reference/inner-products.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Inner-Products Between Networks — inner-products","text":"","code":"g1 <- igraph::sample_gnp(20, 0.1) g2 <- igraph::sample_gnp(20, 0.2) ipro_frobenius(g1, g2, \"adjacency\") #> [1] 8"},{"path":"https://astamm.github.io/nevada/reference/mean.nvd.html","id":null,"dir":"Reference","previous_headings":"","what":"Fréchet Mean of Network-Valued Data — mean.nvd","title":"Fréchet Mean of Network-Valued Data — mean.nvd","text":"function computes sample Fréchet mean observed sample network-valued random variables according specified matrix representation. currently supports Euclidean geometry .e. sample Fréchet mean obtained argmin sum squared Frobenius distances.","code":""},{"path":"https://astamm.github.io/nevada/reference/mean.nvd.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Fréchet Mean of Network-Valued Data — mean.nvd","text":"","code":"# S3 method for class 'nvd' mean(x, weights = rep(1, length(x)), representation = \"adjacency\", ...)"},{"path":"https://astamm.github.io/nevada/reference/mean.nvd.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Fréchet Mean of Network-Valued Data — mean.nvd","text":"x nvd object. weights numeric vector specifying weights observation (default: equally weighted). representation string specifying graph representation used. Choices adjacency, laplacian, modularity, graphon. Default adjacency. ... argument parsed mean function.","code":""},{"path":"https://astamm.github.io/nevada/reference/mean.nvd.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Fréchet Mean of Network-Valued Data — mean.nvd","text":"mean network chosen matrix representation assuming Euclidean geometry now.","code":""},{"path":"https://astamm.github.io/nevada/reference/mean.nvd.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Fréchet Mean of Network-Valued Data — mean.nvd","text":"","code":"params <- list(n = 24L, p = 1/3) x <- nvd(sample_size = 1L, model = \"gnp\", !!!params) #> ℹ Calling the `tidygraph::play_gnp()` function with the following arguments: #> • n: 24 #> • p: 0.333333333333333 #> • directed: TRUE #> • loops: FALSE mean(x) #> [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12] [,13] #> [1,] 0 0 0 0 0 1 0 0 0 1 0 0 1 #> [2,] 1 0 0 1 1 0 1 1 0 0 1 0 1 #> [3,] 1 0 0 1 0 1 0 0 1 0 1 0 0 #> [4,] 0 1 0 0 0 0 1 0 1 1 0 1 0 #> [5,] 0 0 0 0 0 1 0 1 0 0 0 1 1 #> [6,] 0 0 0 0 1 0 1 0 1 0 0 0 0 #> [7,] 0 0 0 1 1 1 0 1 0 0 0 0 0 #> [8,] 1 0 1 0 0 0 1 0 0 0 0 0 0 #> [9,] 0 0 0 0 0 0 1 1 0 0 0 0 1 #> [10,] 1 0 0 0 0 1 1 1 0 0 0 1 0 #> [11,] 0 1 0 1 0 1 0 1 1 1 0 0 0 #> [12,] 0 0 1 1 0 1 1 1 0 0 1 0 1 #> [13,] 0 0 1 0 0 0 0 1 1 1 1 1 0 #> [14,] 1 0 0 0 1 0 0 0 1 1 1 0 1 #> [15,] 0 0 0 0 0 1 1 0 1 0 0 0 0 #> [16,] 0 0 0 0 0 0 0 0 0 0 0 0 0 #> [17,] 0 1 0 0 0 0 0 0 0 0 1 0 0 #> [18,] 0 0 0 1 0 1 1 1 1 1 0 1 0 #> [19,] 1 0 0 1 0 0 1 1 1 0 1 0 1 #> [20,] 0 1 0 0 0 0 0 0 0 0 0 1 0 #> [21,] 1 0 0 0 1 0 0 1 0 0 1 1 1 #> [22,] 0 0 0 0 1 1 0 0 0 1 1 1 0 #> [23,] 0 0 0 0 0 0 0 0 0 0 0 0 0 #> [24,] 0 0 0 1 0 1 1 0 0 0 0 0 0 #> [,14] [,15] [,16] [,17] [,18] [,19] [,20] [,21] [,22] [,23] [,24] #> [1,] 0 0 0 1 0 0 0 0 1 0 0 #> [2,] 0 0 0 0 1 0 1 1 1 1 1 #> [3,] 0 0 1 0 0 0 0 0 1 0 1 #> [4,] 1 0 0 1 0 0 0 1 0 0 0 #> [5,] 1 0 0 1 1 0 1 0 0 0 0 #> [6,] 1 0 0 1 0 0 0 0 0 1 0 #> [7,] 1 0 1 0 0 0 0 1 0 0 0 #> [8,] 0 0 0 0 1 1 1 0 1 1 0 #> [9,] 0 0 0 0 1 1 0 0 0 1 1 #> [10,] 0 1 1 0 0 1 0 0 1 1 0 #> [11,] 0 0 0 1 0 0 0 0 0 1 0 #> [12,] 1 1 0 0 1 0 1 0 0 1 1 #> [13,] 0 1 0 1 1 0 0 0 0 0 0 #> [14,] 0 0 0 0 0 1 0 0 1 0 0 #> [15,] 0 0 0 1 0 0 0 0 1 0 1 #> [16,] 0 0 0 0 0 0 1 0 0 0 1 #> [17,] 1 1 0 0 0 0 0 1 0 1 0 #> [18,] 0 1 0 0 0 0 0 1 1 0 0 #> [19,] 0 0 1 0 0 0 0 1 0 0 0 #> [20,] 0 0 0 0 1 1 0 0 1 1 1 #> [21,] 0 0 0 0 1 0 1 0 1 0 1 #> [22,] 1 1 0 0 0 0 0 0 0 0 1 #> [23,] 0 1 0 0 1 0 0 0 0 0 0 #> [24,] 0 1 0 0 0 1 0 0 0 0 0 #> attr(,\"representation\") #> [1] \"adjacency\""},{"path":"https://astamm.github.io/nevada/reference/nevada-package.html","id":null,"dir":"Reference","previous_headings":"","what":"nevada: Network-Valued Data Analysis — nevada-package","title":"nevada: Network-Valued Data Analysis — nevada-package","text":"flexible statistical framework network-valued data analysis. leverages complexity space distributions graphs using permutation framework inference implemented 'flipr' package. Currently, two-sample testing problem covered generalization k samples regression added future well. 4-step procedure user chooses suitable representation networks, suitable metric embed representation metric space, one test statistics target specific aspects distributions compared formula compute permutation p-value. Two types inference provided: global test answering whether difference distributions generated two samples local test localizing differences network structure. latter assumed shared networks samples. References: Lovato, ., Pini, ., Stamm, ., Vantini, S. (2020) \"Model-free two-sample test network-valued data\" doi:10.1016/j.csda.2019.106896 ; Lovato, ., Pini, ., Stamm, ., Taquet, M., Vantini, S. (2021) \"Multiscale null hypothesis testing network-valued data: Analysis brain networks patients autism\" doi:10.1111/rssc.12463 .","code":""},{"path":[]},{"path":"https://astamm.github.io/nevada/reference/nevada-package.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"nevada: Network-Valued Data Analysis — nevada-package","text":"Maintainer: Aymeric Stamm aymeric.stamm@cnrs.fr (ORCID) Authors: Ilenia Lovato ilenia.lovato01@universitadipavia.Alessia Pini alessia.pini@unicatt.Simone Vantini simone.vantini@polimi.","code":""},{"path":"https://astamm.github.io/nevada/reference/nvd-plot.html","id":null,"dir":"Reference","previous_headings":"","what":"MDS Visualization of Network Distributions — nvd-plot","title":"MDS Visualization of Network Distributions — nvd-plot","text":"function generates 2-dimensional plots samples networks via multi-dimensional scaling using representations distances included package.","code":""},{"path":"https://astamm.github.io/nevada/reference/nvd-plot.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"MDS Visualization of Network Distributions — nvd-plot","text":"","code":"# S3 method for class 'nvd' autoplot(object, memberships = rep(1, length(object)), method = \"mds\", ...) # S3 method for class 'nvd' plot(x, method = \"mds\", ...)"},{"path":"https://astamm.github.io/nevada/reference/nvd-plot.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"MDS Visualization of Network Distributions — nvd-plot","text":"object, x list containing two samples network-valued data stored objects class nvd. memberships integer vector specifying membership network specific sample. Defaults rep(1, length(nvd)) assumes networks input nvd object belong single group. method string specifying dimensionality reduction method use projecting samples cartesian plane. Choices \"mds\", \"tsne\" \"umap\". Defaults \"mds\". ... Extra arguments passed plot function.","code":""},{"path":"https://astamm.github.io/nevada/reference/nvd-plot.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"MDS Visualization of Network Distributions — nvd-plot","text":"Invisibly returns ggplot object. particular, data set computed generate plot can retrieved via $data. tibble containing following variables: V1: x-coordinate observation plane, V2: y-coordinate observation plane, Label: sample membership observation, Representation: type matrix representation used manipulate observation, Distance: distance used measure far observation others.","code":""},{"path":"https://astamm.github.io/nevada/reference/nvd-plot.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"MDS Visualization of Network Distributions — nvd-plot","text":"","code":"gnp_params <- list(n = 24L, p = 1/3) degree_params <- list(out_degree = rep(2, 24L), method = \"configuration\") x <- nvd(sample_size = 10L, model = \"gnp\", !!!gnp_params) #> ℹ Calling the `tidygraph::play_gnp()` function with the following arguments: #> • n: 24 #> • p: 0.333333333333333 #> • directed: TRUE #> • loops: FALSE y <- nvd(sample_size = 10L, model = \"degree\", !!!degree_params) #> ℹ Calling the `tidygraph::play_degree()` function with the following arguments: #> • out_degree: 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, …, 2, and 2 #> • method: configuration #> • in_degree: NULL mb <- c(rep(1, length(x)), rep(2, length(y))) z <- as_nvd(c(x, y)) ggplot2::autoplot(z, memberships = mb) plot(z, memberships = mb)"},{"path":"https://astamm.github.io/nevada/reference/nvd.html","id":null,"dir":"Reference","previous_headings":"","what":"Network-Valued Data Constructor — nvd","title":"Network-Valued Data Constructor — nvd","text":"constructor objects class nvd.","code":""},{"path":"https://astamm.github.io/nevada/reference/nvd.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Network-Valued Data Constructor — nvd","text":"","code":"nvd(sample_size, model, ...)"},{"path":"https://astamm.github.io/nevada/reference/nvd.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Network-Valued Data Constructor — nvd","text":"sample_size integer specifying sample size. model string specifying model used sampling networks. tidygraph::play_ functions supported. model name corresponds name function without play_ prefix. ... Model parameters passed model function.","code":""},{"path":"https://astamm.github.io/nevada/reference/nvd.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Network-Valued Data Constructor — nvd","text":"nvd object list tidygraph::tbl_graph objects.","code":""},{"path":"https://astamm.github.io/nevada/reference/nvd.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Network-Valued Data Constructor — nvd","text":"","code":"params <- list(n_dim = 1L, dim_size = 4L, order = 4L, p_rewire = 0.15) nvd(sample_size = 1L, model = \"smallworld\", !!!params) #> ℹ Calling the `tidygraph::play_smallworld()` function with the following arguments: #> • n_dim: 1 #> • dim_size: 4 #> • order: 4 #> • p_rewire: 0.15 #> • loops: FALSE #> • multiple: FALSE #> [[1]] #> # A tbl_graph: 4 nodes and 6 edges #> # #> # An undirected simple graph with 1 component #> # #> # Node Data: 4 × 0 (active) #> # #> # Edge Data: 6 × 2 #> from to #> #> 1 1 2 #> 2 2 3 #> 3 3 4 #> # ℹ 3 more rows #> #> attr(,\"class\") #> [1] \"nvd\" \"list\""},{"path":"https://astamm.github.io/nevada/reference/power2.html","id":null,"dir":"Reference","previous_headings":"","what":"Power Simulations for Permutation Tests — power2","title":"Power Simulations for Permutation Tests — power2","text":"function provides Monte-Carlo estimate power permutation tests proposed package.","code":""},{"path":"https://astamm.github.io/nevada/reference/power2.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Power Simulations for Permutation Tests — power2","text":"","code":"power2( sample_size1, model1, params1, sample_size2, model2, params2, representation = \"adjacency\", distance = \"frobenius\", stats = c(\"flipr:t_ip\", \"flipr:f_ip\"), B = 1000L, alpha = 0.05, test = \"exact\", k = 5L, R = 1000L )"},{"path":"https://astamm.github.io/nevada/reference/power2.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Power Simulations for Permutation Tests — power2","text":"sample_size1 integer specifying size first sample. model1 string specifying model used sampling networks first sample. tidygraph::play_ functions supported. model name corresponds name function without play_ prefix. params1 list specifying parameters passed model function generate first sample. sample_size2 integer specifying size second sample. model2 string specifying model used sampling networks second sample. tidygraph::play_ functions supported. model name corresponds name function without play_ prefix. params2 list specifying parameters passed model representation string specifying desired type representation, among: \"adjacency\", \"laplacian\" \"modularity\". Defaults \"adjacency\". distance string specifying chosen distance calculating test statistic, among: \"hamming\", \"frobenius\", \"spectral\" \"root-euclidean\". Defaults \"frobenius\". stats character vector specifying chosen test statistic(s), among: \"original_edge_count\", \"generalized_edge_count\", \"weighted_edge_count\", \"student_euclidean\", \"welch_euclidean\" statistics based inter-point distances available flipr package: \"flipr:student_ip\", \"flipr:fisher_ip\", \"flipr:bg_ip\", \"flipr:energy_ip\", \"flipr:cq_ip\". Defaults c(\"flipr:student_ip\", \"flipr:fisher_ip\"). B number permutation tolerance. number lower 1, intended tolerance. Otherwise, intended number required permutations. Defaults 1000L. alpha Significance level hypothesis testing. Defaults 0.05. test character string specifying formula used compute permutation p-value. Choices \"estimate\", \"upper_bound\" \"exact\". Defaults \"exact\" provides exact tests. k integer specifying density minimum spanning tree used edge count statistics. Defaults 5L. R Number Monte-Carlo trials used estimate power. Defaults 1000L.","code":""},{"path":"https://astamm.github.io/nevada/reference/power2.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Power Simulations for Permutation Tests — power2","text":"numeric value estimating power test.","code":""},{"path":"https://astamm.github.io/nevada/reference/power2.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Power Simulations for Permutation Tests — power2","text":"Currently, six scenarios pairs populations implemented. Scenario 0 allows make sure permutation tests exact.","code":""},{"path":"https://astamm.github.io/nevada/reference/power2.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Power Simulations for Permutation Tests — power2","text":"","code":"gnp_params <- list(n = 24L, p = 1/3) degree_params <- list(out_degree = rep(2, 24L), method = \"configuration\") power2( sample_size1 = 10L, model1 = \"gnp\", params1 = gnp_params, sample_size2 = 10L, model2 = \"degree\", params2 = degree_params, R = 10L, B = 100L ) #> ℹ Calling the `tidygraph::play_gnp()` function with the following arguments: #> • n: 24 #> • p: 0.333333333333333 #> • directed: TRUE #> • loops: FALSE #> ℹ Calling the `tidygraph::play_degree()` function with the following arguments: #> • out_degree: 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, …, 2, and 2 #> • method: configuration #> • in_degree: NULL #> ! Setting the seed for sampling permutations is mandatory for obtaining a continuous p-value function. Using `seed = 1234`. #> ℹ Calling the `tidygraph::play_gnp()` function with the following arguments: #> • n: 24 #> • p: 0.333333333333333 #> • directed: TRUE #> • loops: FALSE #> ℹ Calling the `tidygraph::play_degree()` function with the following arguments: #> • out_degree: 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, …, 2, and 2 #> • method: configuration #> • in_degree: NULL #> ! Setting the seed for sampling permutations is mandatory for obtaining a continuous p-value function. Using `seed = 1234`. #> ℹ Calling the `tidygraph::play_gnp()` function with the following arguments: #> • n: 24 #> • p: 0.333333333333333 #> • directed: TRUE #> • loops: FALSE #> ℹ Calling the `tidygraph::play_degree()` function with the following arguments: #> • out_degree: 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, …, 2, and 2 #> • method: configuration #> • in_degree: NULL #> ! Setting the seed for sampling permutations is mandatory for obtaining a continuous p-value function. Using `seed = 1234`. #> ℹ Calling the `tidygraph::play_gnp()` function with the following arguments: #> • n: 24 #> • p: 0.333333333333333 #> • directed: TRUE #> • loops: FALSE #> ℹ Calling the `tidygraph::play_degree()` function with the following arguments: #> • out_degree: 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, …, 2, and 2 #> • method: configuration #> • in_degree: NULL #> ! Setting the seed for sampling permutations is mandatory for obtaining a continuous p-value function. Using `seed = 1234`. #> ℹ Calling the `tidygraph::play_gnp()` function with the following arguments: #> • n: 24 #> • p: 0.333333333333333 #> • directed: TRUE #> • loops: FALSE #> ℹ Calling the `tidygraph::play_degree()` function with the following arguments: #> • out_degree: 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, …, 2, and 2 #> • method: configuration #> • in_degree: NULL #> ! Setting the seed for sampling permutations is mandatory for obtaining a continuous p-value function. Using `seed = 1234`. #> ℹ Calling the `tidygraph::play_gnp()` function with the following arguments: #> • n: 24 #> • p: 0.333333333333333 #> • directed: TRUE #> • loops: FALSE #> ℹ Calling the `tidygraph::play_degree()` function with the following arguments: #> • out_degree: 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, …, 2, and 2 #> • method: configuration #> • in_degree: NULL #> ! Setting the seed for sampling permutations is mandatory for obtaining a continuous p-value function. Using `seed = 1234`. #> ℹ Calling the `tidygraph::play_gnp()` function with the following arguments: #> • n: 24 #> • p: 0.333333333333333 #> • directed: TRUE #> • loops: FALSE #> ℹ Calling the `tidygraph::play_degree()` function with the following arguments: #> • out_degree: 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, …, 2, and 2 #> • method: configuration #> • in_degree: NULL #> ! Setting the seed for sampling permutations is mandatory for obtaining a continuous p-value function. Using `seed = 1234`. #> ℹ Calling the `tidygraph::play_gnp()` function with the following arguments: #> • n: 24 #> • p: 0.333333333333333 #> • directed: TRUE #> • loops: FALSE #> ℹ Calling the `tidygraph::play_degree()` function with the following arguments: #> • out_degree: 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, …, 2, and 2 #> • method: configuration #> • in_degree: NULL #> ! Setting the seed for sampling permutations is mandatory for obtaining a continuous p-value function. Using `seed = 1234`. #> ℹ Calling the `tidygraph::play_gnp()` function with the following arguments: #> • n: 24 #> • p: 0.333333333333333 #> • directed: TRUE #> • loops: FALSE #> ℹ Calling the `tidygraph::play_degree()` function with the following arguments: #> • out_degree: 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, …, 2, and 2 #> • method: configuration #> • in_degree: NULL #> ! Setting the seed for sampling permutations is mandatory for obtaining a continuous p-value function. Using `seed = 1234`. #> ℹ Calling the `tidygraph::play_gnp()` function with the following arguments: #> • n: 24 #> • p: 0.333333333333333 #> • directed: TRUE #> • loops: FALSE #> ℹ Calling the `tidygraph::play_degree()` function with the following arguments: #> • out_degree: 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, …, 2, and 2 #> • method: configuration #> • in_degree: NULL #> ! Setting the seed for sampling permutations is mandatory for obtaining a continuous p-value function. Using `seed = 1234`. #> [1] 1"},{"path":"https://astamm.github.io/nevada/reference/push_to_graph_space.html","id":null,"dir":"Reference","previous_headings":"","what":"Graph Sample Embeddings — push_to_graph_space","title":"Graph Sample Embeddings — push_to_graph_space","text":"collection functions embed sample graphs suitable spaces statistical analysis.","code":""},{"path":"https://astamm.github.io/nevada/reference/push_to_graph_space.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Graph Sample Embeddings — push_to_graph_space","text":"","code":"push_to_graph_space(obj)"},{"path":"https://astamm.github.io/nevada/reference/push_to_graph_space.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Graph Sample Embeddings — push_to_graph_space","text":"obj object class nvd containing sample graphs.","code":""},{"path":"https://astamm.github.io/nevada/reference/push_to_graph_space.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Graph Sample Embeddings — push_to_graph_space","text":"object class nvd containing sample graphs graph space.","code":""},{"path":"https://astamm.github.io/nevada/reference/push_to_graph_space.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Graph Sample Embeddings — push_to_graph_space","text":"","code":"x <- nvd(sample_size = 5L, model = \"gnp\", n = 24L, p = 1/3) #> ℹ Calling the `tidygraph::play_gnp()` function with the following arguments: #> • n: 24 #> • p: 0.333333333333333 #> • directed: TRUE #> • loops: FALSE x <- push_to_graph_space(x) #> ℹ Graphs have the following number of vertices: 24, 24, 24, 24, and 24"},{"path":"https://astamm.github.io/nevada/reference/repr_nvd.html","id":null,"dir":"Reference","previous_headings":"","what":"Network-Valued to Matrix-Valued Data — repr_nvd","title":"Network-Valued to Matrix-Valued Data — repr_nvd","text":"Network-Valued Matrix-Valued Data","code":""},{"path":"https://astamm.github.io/nevada/reference/repr_nvd.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Network-Valued to Matrix-Valued Data — repr_nvd","text":"","code":"repr_nvd(x, y = NULL, representation = \"adjacency\")"},{"path":"https://astamm.github.io/nevada/reference/repr_nvd.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Network-Valued to Matrix-Valued Data — repr_nvd","text":"x nvd object. y nvd object. NULL (default), taken account. representation string specifying requested matrix representation. Choices : \"adjacency\", \"laplacian\" \"modularity\". Default \"adjacency\".","code":""},{"path":"https://astamm.github.io/nevada/reference/repr_nvd.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Network-Valued to Matrix-Valued Data — repr_nvd","text":"list matrices.","code":""},{"path":"https://astamm.github.io/nevada/reference/repr_nvd.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Network-Valued to Matrix-Valued Data — repr_nvd","text":"","code":"params <- list(n = 24L, p = 1/3) x <- nvd(sample_size = 1L, model = \"gnp\", !!!params) #> ℹ Calling the `tidygraph::play_gnp()` function with the following arguments: #> • n: 24 #> • p: 0.333333333333333 #> • directed: TRUE #> • loops: FALSE xm <- repr_nvd(x)"},{"path":"https://astamm.github.io/nevada/reference/representations.html","id":null,"dir":"Reference","previous_headings":"","what":"Network Representation Functions — representations","title":"Network Representation Functions — representations","text":"collection functions convert graph stored igraph object desired matrix representation among adjacency matrix, graph laplacian, modularity matrix graphon (edge probability matrix).","code":""},{"path":"https://astamm.github.io/nevada/reference/representations.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Network Representation Functions — representations","text":"","code":"repr_adjacency(network, validate = TRUE) repr_laplacian(network, validate = TRUE) repr_modularity(network, validate = TRUE) repr_graphon(network, validate = TRUE)"},{"path":"https://astamm.github.io/nevada/reference/representations.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Network Representation Functions — representations","text":"network igraph object. validate boolean specifying whether function check class input (default: TRUE).","code":""},{"path":"https://astamm.github.io/nevada/reference/representations.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Network Representation Functions — representations","text":"numeric square matrix giving desired network representation recorded object's class.","code":""},{"path":"https://astamm.github.io/nevada/reference/representations.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Network Representation Functions — representations","text":"","code":"g <- igraph::sample_smallworld(1, 25, 3, 0.05) repr_adjacency(g) #> [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12] [,13] #> [1,] 0 1 1 1 0 0 0 0 0 0 0 0 0 #> [2,] 1 0 1 1 1 0 0 0 0 0 0 0 0 #> [3,] 1 1 0 1 1 1 0 0 0 0 0 0 0 #> [4,] 1 1 1 0 1 1 1 0 0 0 0 0 0 #> [5,] 0 1 1 1 0 1 1 1 0 0 0 0 0 #> [6,] 0 0 1 1 1 0 1 1 1 0 0 0 0 #> [7,] 0 0 0 1 1 1 0 1 1 1 0 0 0 #> [8,] 0 0 0 0 1 1 1 0 1 1 1 0 0 #> [9,] 0 0 0 0 0 1 1 1 0 1 1 1 0 #> [10,] 0 0 0 0 0 0 1 1 1 0 1 1 1 #> [11,] 0 0 0 0 0 0 0 1 1 1 0 1 1 #> [12,] 0 0 0 0 0 0 0 0 1 1 1 0 1 #> [13,] 0 0 0 0 0 0 0 0 0 1 1 1 0 #> [14,] 0 0 0 0 0 0 0 0 0 0 0 1 1 #> [15,] 0 0 0 0 0 0 0 0 0 0 0 1 1 #> [16,] 0 0 0 0 0 0 0 0 0 0 0 0 1 #> [17,] 0 0 0 0 0 0 0 0 0 0 1 0 0 #> [18,] 0 0 0 0 0 0 0 0 0 0 0 0 0 #> [19,] 0 0 0 0 0 0 0 0 0 0 0 0 0 #> [20,] 0 0 0 0 0 0 0 0 0 0 0 0 0 #> [21,] 0 0 0 0 0 0 0 0 0 0 0 0 0 #> [22,] 0 0 0 0 0 0 0 0 0 0 0 0 0 #> [23,] 1 0 0 0 0 0 0 0 0 0 0 0 0 #> [24,] 1 1 0 0 0 0 0 0 0 0 0 0 0 #> [25,] 1 1 0 0 0 0 0 0 0 0 1 0 0 #> [,14] [,15] [,16] [,17] [,18] [,19] [,20] [,21] [,22] [,23] [,24] [,25] #> [1,] 0 0 0 0 0 0 0 0 0 1 1 1 #> [2,] 0 0 0 0 0 0 0 0 0 0 1 1 #> [3,] 0 0 0 0 0 0 0 0 0 0 0 0 #> [4,] 0 0 0 0 0 0 0 0 0 0 0 0 #> [5,] 0 0 0 0 0 0 0 0 0 0 0 0 #> [6,] 0 0 0 0 0 0 0 0 0 0 0 0 #> [7,] 0 0 0 0 0 0 0 0 0 0 0 0 #> [8,] 0 0 0 0 0 0 0 0 0 0 0 0 #> [9,] 0 0 0 0 0 0 0 0 0 0 0 0 #> [10,] 0 0 0 0 0 0 0 0 0 0 0 0 #> [11,] 0 0 0 1 0 0 0 0 0 0 0 1 #> [12,] 1 1 0 0 0 0 0 0 0 0 0 0 #> [13,] 1 1 1 0 0 0 0 0 0 0 0 0 #> [14,] 0 1 1 1 0 0 0 0 0 0 0 0 #> [15,] 1 0 1 1 0 0 0 0 0 1 0 0 #> [16,] 1 1 0 1 1 1 0 0 0 0 0 0 #> [17,] 1 1 1 0 1 1 1 1 0 0 0 0 #> [18,] 0 0 1 1 0 1 1 1 0 0 0 0 #> [19,] 0 0 1 1 1 0 1 1 1 0 0 0 #> [20,] 0 0 0 1 1 1 0 0 1 1 0 0 #> [21,] 0 0 0 1 1 1 0 0 1 1 1 0 #> [22,] 0 0 0 0 0 1 1 1 0 1 1 1 #> [23,] 0 1 0 0 0 0 1 1 1 0 1 1 #> [24,] 0 0 0 0 0 0 0 1 1 1 0 1 #> [25,] 0 0 0 0 0 0 0 0 1 1 1 0 #> attr(,\"representation\") #> [1] \"adjacency\" repr_laplacian(g) #> [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12] [,13] #> [1,] 6 -1 -1 -1 0 0 0 0 0 0 0 0 0 #> [2,] -1 6 -1 -1 -1 0 0 0 0 0 0 0 0 #> [3,] -1 -1 5 -1 -1 -1 0 0 0 0 0 0 0 #> [4,] -1 -1 -1 6 -1 -1 -1 0 0 0 0 0 0 #> [5,] 0 -1 -1 -1 6 -1 -1 -1 0 0 0 0 0 #> [6,] 0 0 -1 -1 -1 6 -1 -1 -1 0 0 0 0 #> [7,] 0 0 0 -1 -1 -1 6 -1 -1 -1 0 0 0 #> [8,] 0 0 0 0 -1 -1 -1 6 -1 -1 -1 0 0 #> [9,] 0 0 0 0 0 -1 -1 -1 6 -1 -1 -1 0 #> [10,] 0 0 0 0 0 0 -1 -1 -1 6 -1 -1 -1 #> [11,] 0 0 0 0 0 0 0 -1 -1 -1 7 -1 -1 #> [12,] 0 0 0 0 0 0 0 0 -1 -1 -1 6 -1 #> [13,] 0 0 0 0 0 0 0 0 0 -1 -1 -1 6 #> [14,] 0 0 0 0 0 0 0 0 0 0 0 -1 -1 #> [15,] 0 0 0 0 0 0 0 0 0 0 0 -1 -1 #> [16,] 0 0 0 0 0 0 0 0 0 0 0 0 -1 #> [17,] 0 0 0 0 0 0 0 0 0 0 -1 0 0 #> [18,] 0 0 0 0 0 0 0 0 0 0 0 0 0 #> [19,] 0 0 0 0 0 0 0 0 0 0 0 0 0 #> [20,] 0 0 0 0 0 0 0 0 0 0 0 0 0 #> [21,] 0 0 0 0 0 0 0 0 0 0 0 0 0 #> [22,] 0 0 0 0 0 0 0 0 0 0 0 0 0 #> [23,] -1 0 0 0 0 0 0 0 0 0 0 0 0 #> [24,] -1 -1 0 0 0 0 0 0 0 0 0 0 0 #> [25,] -1 -1 0 0 0 0 0 0 0 0 -1 0 0 #> [,14] [,15] [,16] [,17] [,18] [,19] [,20] [,21] [,22] [,23] [,24] [,25] #> [1,] 0 0 0 0 0 0 0 0 0 -1 -1 -1 #> [2,] 0 0 0 0 0 0 0 0 0 0 -1 -1 #> [3,] 0 0 0 0 0 0 0 0 0 0 0 0 #> [4,] 0 0 0 0 0 0 0 0 0 0 0 0 #> [5,] 0 0 0 0 0 0 0 0 0 0 0 0 #> [6,] 0 0 0 0 0 0 0 0 0 0 0 0 #> [7,] 0 0 0 0 0 0 0 0 0 0 0 0 #> [8,] 0 0 0 0 0 0 0 0 0 0 0 0 #> [9,] 0 0 0 0 0 0 0 0 0 0 0 0 #> [10,] 0 0 0 0 0 0 0 0 0 0 0 0 #> [11,] 0 0 0 -1 0 0 0 0 0 0 0 -1 #> [12,] -1 -1 0 0 0 0 0 0 0 0 0 0 #> [13,] -1 -1 -1 0 0 0 0 0 0 0 0 0 #> [14,] 5 -1 -1 -1 0 0 0 0 0 0 0 0 #> [15,] -1 6 -1 -1 0 0 0 0 0 -1 0 0 #> [16,] -1 -1 6 -1 -1 -1 0 0 0 0 0 0 #> [17,] -1 -1 -1 8 -1 -1 -1 -1 0 0 0 0 #> [18,] 0 0 -1 -1 5 -1 -1 -1 0 0 0 0 #> [19,] 0 0 -1 -1 -1 6 -1 -1 -1 0 0 0 #> [20,] 0 0 0 -1 -1 -1 5 0 -1 -1 0 0 #> [21,] 0 0 0 -1 -1 -1 0 6 -1 -1 -1 0 #> [22,] 0 0 0 0 0 -1 -1 -1 6 -1 -1 -1 #> [23,] 0 -1 0 0 0 0 -1 -1 -1 7 -1 -1 #> [24,] 0 0 0 0 0 0 0 -1 -1 -1 6 -1 #> [25,] 0 0 0 0 0 0 0 0 -1 -1 -1 6 #> attr(,\"representation\") #> [1] \"laplacian\" repr_modularity(g) #> [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] #> [1,] -0.24 0.76 0.8000000 0.76 -0.24 -0.24 -0.24 -0.24 -0.24 -0.24 #> [2,] 0.76 -0.24 0.8000000 0.76 0.76 -0.24 -0.24 -0.24 -0.24 -0.24 #> [3,] 0.80 0.80 -0.1666667 0.80 0.80 0.80 -0.20 -0.20 -0.20 -0.20 #> [4,] 0.76 0.76 0.8000000 -0.24 0.76 0.76 0.76 -0.24 -0.24 -0.24 #> [5,] -0.24 0.76 0.8000000 0.76 -0.24 0.76 0.76 0.76 -0.24 -0.24 #> [6,] -0.24 -0.24 0.8000000 0.76 0.76 -0.24 0.76 0.76 0.76 -0.24 #> [7,] -0.24 -0.24 -0.2000000 0.76 0.76 0.76 -0.24 0.76 0.76 0.76 #> [8,] -0.24 -0.24 -0.2000000 -0.24 0.76 0.76 0.76 -0.24 0.76 0.76 #> [9,] -0.24 -0.24 -0.2000000 -0.24 -0.24 0.76 0.76 0.76 -0.24 0.76 #> [10,] -0.24 -0.24 -0.2000000 -0.24 -0.24 -0.24 0.76 0.76 0.76 -0.24 #> [11,] -0.28 -0.28 -0.2333333 -0.28 -0.28 -0.28 -0.28 0.72 0.72 0.72 #> [12,] -0.24 -0.24 -0.2000000 -0.24 -0.24 -0.24 -0.24 -0.24 0.76 0.76 #> [13,] -0.24 -0.24 -0.2000000 -0.24 -0.24 -0.24 -0.24 -0.24 -0.24 0.76 #> [14,] -0.20 -0.20 -0.1666667 -0.20 -0.20 -0.20 -0.20 -0.20 -0.20 -0.20 #> [15,] -0.24 -0.24 -0.2000000 -0.24 -0.24 -0.24 -0.24 -0.24 -0.24 -0.24 #> [16,] -0.24 -0.24 -0.2000000 -0.24 -0.24 -0.24 -0.24 -0.24 -0.24 -0.24 #> [17,] -0.32 -0.32 -0.2666667 -0.32 -0.32 -0.32 -0.32 -0.32 -0.32 -0.32 #> [18,] -0.20 -0.20 -0.1666667 -0.20 -0.20 -0.20 -0.20 -0.20 -0.20 -0.20 #> [19,] -0.24 -0.24 -0.2000000 -0.24 -0.24 -0.24 -0.24 -0.24 -0.24 -0.24 #> [20,] -0.20 -0.20 -0.1666667 -0.20 -0.20 -0.20 -0.20 -0.20 -0.20 -0.20 #> [21,] -0.24 -0.24 -0.2000000 -0.24 -0.24 -0.24 -0.24 -0.24 -0.24 -0.24 #> [22,] -0.24 -0.24 -0.2000000 -0.24 -0.24 -0.24 -0.24 -0.24 -0.24 -0.24 #> [23,] 0.72 -0.28 -0.2333333 -0.28 -0.28 -0.28 -0.28 -0.28 -0.28 -0.28 #> [24,] 0.76 0.76 -0.2000000 -0.24 -0.24 -0.24 -0.24 -0.24 -0.24 -0.24 #> [25,] 0.76 0.76 -0.2000000 -0.24 -0.24 -0.24 -0.24 -0.24 -0.24 -0.24 #> [,11] [,12] [,13] [,14] [,15] [,16] [,17] [,18] [,19] #> [1,] -0.2800000 -0.24 -0.24 -0.2000000 -0.24 -0.24 -0.3200000 -0.2000000 -0.24 #> [2,] -0.2800000 -0.24 -0.24 -0.2000000 -0.24 -0.24 -0.3200000 -0.2000000 -0.24 #> [3,] -0.2333333 -0.20 -0.20 -0.1666667 -0.20 -0.20 -0.2666667 -0.1666667 -0.20 #> [4,] -0.2800000 -0.24 -0.24 -0.2000000 -0.24 -0.24 -0.3200000 -0.2000000 -0.24 #> [5,] -0.2800000 -0.24 -0.24 -0.2000000 -0.24 -0.24 -0.3200000 -0.2000000 -0.24 #> [6,] -0.2800000 -0.24 -0.24 -0.2000000 -0.24 -0.24 -0.3200000 -0.2000000 -0.24 #> [7,] -0.2800000 -0.24 -0.24 -0.2000000 -0.24 -0.24 -0.3200000 -0.2000000 -0.24 #> [8,] 0.7200000 -0.24 -0.24 -0.2000000 -0.24 -0.24 -0.3200000 -0.2000000 -0.24 #> [9,] 0.7200000 0.76 -0.24 -0.2000000 -0.24 -0.24 -0.3200000 -0.2000000 -0.24 #> [10,] 0.7200000 0.76 0.76 -0.2000000 -0.24 -0.24 -0.3200000 -0.2000000 -0.24 #> [11,] -0.3266667 0.72 0.72 -0.2333333 -0.28 -0.28 0.6266667 -0.2333333 -0.28 #> [12,] 0.7200000 -0.24 0.76 0.8000000 0.76 -0.24 -0.3200000 -0.2000000 -0.24 #> [13,] 0.7200000 0.76 -0.24 0.8000000 0.76 0.76 -0.3200000 -0.2000000 -0.24 #> [14,] -0.2333333 0.80 0.80 -0.1666667 0.80 0.80 0.7333333 -0.1666667 -0.20 #> [15,] -0.2800000 0.76 0.76 0.8000000 -0.24 0.76 0.6800000 -0.2000000 -0.24 #> [16,] -0.2800000 -0.24 0.76 0.8000000 0.76 -0.24 0.6800000 0.8000000 0.76 #> [17,] 0.6266667 -0.32 -0.32 0.7333333 0.68 0.68 -0.4266667 0.7333333 0.68 #> [18,] -0.2333333 -0.20 -0.20 -0.1666667 -0.20 0.80 0.7333333 -0.1666667 0.80 #> [19,] -0.2800000 -0.24 -0.24 -0.2000000 -0.24 0.76 0.6800000 0.8000000 -0.24 #> [20,] -0.2333333 -0.20 -0.20 -0.1666667 -0.20 -0.20 0.7333333 0.8333333 0.80 #> [21,] -0.2800000 -0.24 -0.24 -0.2000000 -0.24 -0.24 0.6800000 0.8000000 0.76 #> [22,] -0.2800000 -0.24 -0.24 -0.2000000 -0.24 -0.24 -0.3200000 -0.2000000 0.76 #> [23,] -0.3266667 -0.28 -0.28 -0.2333333 0.72 -0.28 -0.3733333 -0.2333333 -0.28 #> [24,] -0.2800000 -0.24 -0.24 -0.2000000 -0.24 -0.24 -0.3200000 -0.2000000 -0.24 #> [25,] 0.7200000 -0.24 -0.24 -0.2000000 -0.24 -0.24 -0.3200000 -0.2000000 -0.24 #> [,20] [,21] [,22] [,23] [,24] [,25] #> [1,] -0.2000000 -0.24 -0.24 0.7200000 0.76 0.76 #> [2,] -0.2000000 -0.24 -0.24 -0.2800000 0.76 0.76 #> [3,] -0.1666667 -0.20 -0.20 -0.2333333 -0.20 -0.20 #> [4,] -0.2000000 -0.24 -0.24 -0.2800000 -0.24 -0.24 #> [5,] -0.2000000 -0.24 -0.24 -0.2800000 -0.24 -0.24 #> [6,] -0.2000000 -0.24 -0.24 -0.2800000 -0.24 -0.24 #> [7,] -0.2000000 -0.24 -0.24 -0.2800000 -0.24 -0.24 #> [8,] -0.2000000 -0.24 -0.24 -0.2800000 -0.24 -0.24 #> [9,] -0.2000000 -0.24 -0.24 -0.2800000 -0.24 -0.24 #> [10,] -0.2000000 -0.24 -0.24 -0.2800000 -0.24 -0.24 #> [11,] -0.2333333 -0.28 -0.28 -0.3266667 -0.28 0.72 #> [12,] -0.2000000 -0.24 -0.24 -0.2800000 -0.24 -0.24 #> [13,] -0.2000000 -0.24 -0.24 -0.2800000 -0.24 -0.24 #> [14,] -0.1666667 -0.20 -0.20 -0.2333333 -0.20 -0.20 #> [15,] -0.2000000 -0.24 -0.24 0.7200000 -0.24 -0.24 #> [16,] -0.2000000 -0.24 -0.24 -0.2800000 -0.24 -0.24 #> [17,] 0.7333333 0.68 -0.32 -0.3733333 -0.32 -0.32 #> [18,] 0.8333333 0.80 -0.20 -0.2333333 -0.20 -0.20 #> [19,] 0.8000000 0.76 0.76 -0.2800000 -0.24 -0.24 #> [20,] -0.1666667 -0.20 0.80 0.7666667 -0.20 -0.20 #> [21,] -0.2000000 -0.24 0.76 0.7200000 0.76 -0.24 #> [22,] 0.8000000 0.76 -0.24 0.7200000 0.76 0.76 #> [23,] 0.7666667 0.72 0.72 -0.3266667 0.72 0.72 #> [24,] -0.2000000 0.76 0.76 0.7200000 -0.24 0.76 #> [25,] -0.2000000 -0.24 0.76 0.7200000 0.76 -0.24 #> attr(,\"representation\") #> [1] \"modularity\" repr_graphon(g) #> [,1] [,2] [,3] [,4] [,5] [,6] #> [1,] 0.55555556 0.63333333 0.57777778 0.52777778 0.36507937 0.30952381 #> [2,] 0.63333333 0.60000000 0.70000000 0.65000000 0.68571429 0.34285714 #> [3,] 0.57777778 0.70000000 0.60000000 0.73333333 0.68571429 0.68571429 #> [4,] 0.52777778 0.65000000 0.73333333 0.66666667 0.77380952 0.61904762 #> [5,] 0.36507937 0.68571429 0.68571429 0.77380952 0.57142857 0.71428571 #> [6,] 0.30952381 0.34285714 0.68571429 0.61904762 0.71428571 0.57142857 #> [7,] 0.25000000 0.36666667 0.36666667 0.66666667 0.61904762 0.77380952 #> [8,] 0.18253968 0.17142857 0.34285714 0.30952381 0.57142857 0.57142857 #> [9,] 0.11111111 0.21111111 0.26666667 0.33333333 0.36507937 0.56349206 #> [10,] 0.00000000 0.00000000 0.18333333 0.16666667 0.30952381 0.30952381 #> [11,] 0.05555556 0.00000000 0.00000000 0.15476190 0.14285714 0.28571429 #> [12,] 0.00000000 0.00000000 0.00000000 0.05555556 0.18253968 0.23809524 #> [13,] 0.00000000 0.00000000 0.00000000 0.00000000 0.05555556 0.18253968 #> [14,] 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 #> [15,] 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 #> [16,] 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 #> [17,] 0.06250000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 #> [18,] 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 #> [19,] 0.11111111 0.05555556 0.00000000 0.00000000 0.00000000 0.00000000 #> [20,] 0.16666667 0.11111111 0.00000000 0.00000000 0.00000000 0.00000000 #> [21,] 0.22222222 0.11111111 0.00000000 0.00000000 0.00000000 0.00000000 #> [22,] 0.27777778 0.16666667 0.08333333 0.08333333 0.00000000 0.00000000 #> [23,] 0.55555556 0.26666667 0.08333333 0.08333333 0.15476190 0.00000000 #> [24,] 0.52222222 0.50000000 0.20000000 0.18333333 0.07142857 0.07142857 #> [25,] 0.50000000 0.47777778 0.26666667 0.25000000 0.23809524 0.18253968 #> [,7] [,8] [,9] [,10] [,11] [,12] #> [1,] 0.25000000 0.18253968 0.1111111 0.00000000 0.05555556 0.00000000 #> [2,] 0.36666667 0.17142857 0.2111111 0.00000000 0.00000000 0.00000000 #> [3,] 0.36666667 0.34285714 0.2666667 0.18333333 0.00000000 0.00000000 #> [4,] 0.66666667 0.30952381 0.3333333 0.16666667 0.15476190 0.05555556 #> [5,] 0.61904762 0.57142857 0.3650794 0.30952381 0.14285714 0.18253968 #> [6,] 0.77380952 0.57142857 0.5634921 0.30952381 0.28571429 0.23809524 #> [7,] 0.66666667 0.69047619 0.5833333 0.58333333 0.30952381 0.25000000 #> [8,] 0.69047619 0.57142857 0.6349206 0.61904762 0.57142857 0.30952381 #> [9,] 0.58333333 0.63492063 0.5555556 0.69444444 0.56349206 0.38888889 #> [10,] 0.58333333 0.61904762 0.6944444 0.66666667 0.61904762 0.52777778 #> [11,] 0.30952381 0.57142857 0.5634921 0.61904762 0.42857143 0.63492063 #> [12,] 0.25000000 0.30952381 0.3888889 0.52777778 0.63492063 0.55555556 #> [13,] 0.16666667 0.25396825 0.2777778 0.47222222 0.69047619 0.55555556 #> [14,] 0.05555556 0.12698413 0.2222222 0.19444444 0.30952381 0.44444444 #> [15,] 0.00000000 0.07142857 0.1111111 0.20833333 0.26785714 0.59722222 #> [16,] 0.00000000 0.00000000 0.1111111 0.11111111 0.25396825 0.33333333 #> [17,] 0.00000000 0.00000000 0.0625000 0.20833333 0.40178571 0.22916667 #> [18,] 0.00000000 0.00000000 0.0000000 0.00000000 0.05555556 0.16666667 #> [19,] 0.00000000 0.00000000 0.0000000 0.00000000 0.00000000 0.16666667 #> [20,] 0.00000000 0.00000000 0.0000000 0.00000000 0.05555556 0.05555556 #> [21,] 0.00000000 0.00000000 0.0000000 0.00000000 0.05555556 0.05555556 #> [22,] 0.00000000 0.00000000 0.0000000 0.00000000 0.00000000 0.00000000 #> [23,] 0.00000000 0.00000000 0.0000000 0.00000000 0.15476190 0.05555556 #> [24,] 0.00000000 0.00000000 0.0000000 0.00000000 0.10000000 0.00000000 #> [25,] 0.05555556 0.00000000 0.0000000 0.08333333 0.12698413 0.00000000 #> [,13] [,14] [,15] [,16] [,17] [,18] #> [1,] 0.00000000 0.00000000 0.00000000 0.00000000 0.0625000 0.00000000 #> [2,] 0.00000000 0.00000000 0.00000000 0.00000000 0.0000000 0.00000000 #> [3,] 0.00000000 0.00000000 0.00000000 0.00000000 0.0000000 0.00000000 #> [4,] 0.00000000 0.00000000 0.00000000 0.00000000 0.0000000 0.00000000 #> [5,] 0.05555556 0.00000000 0.00000000 0.00000000 0.0000000 0.00000000 #> [6,] 0.18253968 0.00000000 0.00000000 0.00000000 0.0000000 0.00000000 #> [7,] 0.16666667 0.05555556 0.00000000 0.00000000 0.0000000 0.00000000 #> [8,] 0.25396825 0.12698413 0.07142857 0.00000000 0.0000000 0.00000000 #> [9,] 0.27777778 0.22222222 0.11111111 0.11111111 0.0625000 0.00000000 #> [10,] 0.47222222 0.19444444 0.20833333 0.11111111 0.2083333 0.00000000 #> [11,] 0.69047619 0.30952381 0.26785714 0.25396825 0.4017857 0.05555556 #> [12,] 0.55555556 0.44444444 0.59722222 0.33333333 0.2291667 0.16666667 #> [13,] 0.55555556 0.55555556 0.65277778 0.44444444 0.2916667 0.27777778 #> [14,] 0.55555556 0.44444444 0.59722222 0.50000000 0.5833333 0.33333333 #> [15,] 0.65277778 0.59722222 0.75000000 0.59722222 0.6875000 0.29166667 #> [16,] 0.44444444 0.50000000 0.59722222 0.55555556 0.6388889 0.50000000 #> [17,] 0.29166667 0.58333333 0.68750000 0.63888889 0.3750000 0.57638889 #> [18,] 0.27777778 0.33333333 0.29166667 0.50000000 0.5763889 0.55555556 #> [19,] 0.27777778 0.27777778 0.23611111 0.44444444 0.6388889 0.55555556 #> [20,] 0.16666667 0.22222222 0.05555556 0.27777778 0.6458333 0.44444444 #> [21,] 0.16666667 0.22222222 0.05555556 0.27777778 0.6458333 0.44444444 #> [22,] 0.00000000 0.11111111 0.08333333 0.25000000 0.2916667 0.25000000 #> [23,] 0.05555556 0.11111111 0.20833333 0.25000000 0.1458333 0.30555556 #> [24,] 0.00000000 0.00000000 0.10000000 0.05555556 0.1250000 0.11111111 #> [25,] 0.00000000 0.00000000 0.00000000 0.00000000 0.2361111 0.16666667 #> [,19] [,20] [,21] [,22] [,23] [,24] #> [1,] 0.11111111 0.16666667 0.22222222 0.27777778 0.55555556 0.52222222 #> [2,] 0.05555556 0.11111111 0.11111111 0.16666667 0.26666667 0.50000000 #> [3,] 0.00000000 0.00000000 0.00000000 0.08333333 0.08333333 0.20000000 #> [4,] 0.00000000 0.00000000 0.00000000 0.08333333 0.08333333 0.18333333 #> [5,] 0.00000000 0.00000000 0.00000000 0.00000000 0.15476190 0.07142857 #> [6,] 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.07142857 #> [7,] 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 #> [8,] 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 #> [9,] 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 #> [10,] 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 #> [11,] 0.00000000 0.05555556 0.05555556 0.00000000 0.15476190 0.10000000 #> [12,] 0.16666667 0.05555556 0.05555556 0.00000000 0.05555556 0.00000000 #> [13,] 0.27777778 0.16666667 0.16666667 0.00000000 0.05555556 0.00000000 #> [14,] 0.27777778 0.22222222 0.22222222 0.11111111 0.11111111 0.00000000 #> [15,] 0.23611111 0.05555556 0.05555556 0.08333333 0.20833333 0.10000000 #> [16,] 0.44444444 0.27777778 0.27777778 0.25000000 0.25000000 0.05555556 #> [17,] 0.63888889 0.64583333 0.64583333 0.29166667 0.14583333 0.12500000 #> [18,] 0.55555556 0.44444444 0.44444444 0.25000000 0.30555556 0.11111111 #> [19,] 0.55555556 0.44444444 0.50000000 0.47222222 0.36111111 0.21111111 #> [20,] 0.44444444 0.33333333 0.38888889 0.52777778 0.58333333 0.36666667 #> [21,] 0.50000000 0.38888889 0.44444444 0.61111111 0.66666667 0.46666667 #> [22,] 0.47222222 0.52777778 0.61111111 0.50000000 0.66666667 0.63333333 #> [23,] 0.36111111 0.58333333 0.66666667 0.66666667 0.50000000 0.73333333 #> [24,] 0.21111111 0.36666667 0.46666667 0.63333333 0.73333333 0.80000000 #> [25,] 0.27777778 0.16666667 0.22222222 0.55555556 0.66666667 0.67777778 #> [,25] #> [1,] 0.50000000 #> [2,] 0.47777778 #> [3,] 0.26666667 #> [4,] 0.25000000 #> [5,] 0.23809524 #> [6,] 0.18253968 #> [7,] 0.05555556 #> [8,] 0.00000000 #> [9,] 0.00000000 #> [10,] 0.08333333 #> [11,] 0.12698413 #> [12,] 0.00000000 #> [13,] 0.00000000 #> [14,] 0.00000000 #> [15,] 0.00000000 #> [16,] 0.00000000 #> [17,] 0.23611111 #> [18,] 0.16666667 #> [19,] 0.27777778 #> [20,] 0.16666667 #> [21,] 0.22222222 #> [22,] 0.55555556 #> [23,] 0.66666667 #> [24,] 0.67777778 #> [25,] 0.44444444 #> attr(,\"representation\") #> [1] \"graphon\""},{"path":"https://astamm.github.io/nevada/reference/sample2_sbm.html","id":null,"dir":"Reference","previous_headings":"","what":"Two-Sample Stochastic Block Model Generator — sample2_sbm","title":"Two-Sample Stochastic Block Model Generator — sample2_sbm","text":"function generates two samples networks according stochastic block model (SBM). essentially wrapper around sample_sbm allows sample single network SBM.","code":""},{"path":"https://astamm.github.io/nevada/reference/sample2_sbm.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Two-Sample Stochastic Block Model Generator — sample2_sbm","text":"","code":"sample2_sbm(n, nv, p1, b1, p2 = p1, b2 = b1, seed = NULL)"},{"path":"https://astamm.github.io/nevada/reference/sample2_sbm.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Two-Sample Stochastic Block Model Generator — sample2_sbm","text":"n Integer scalar giving sample size. nv Integer scalar giving number vertices generated networks, common networks samples. p1 matrix giving Bernoulli rates 1st sample. KxK matrix, K number groups. probability creating edge vertices groups j given element (,j). undirected graphs, matrix must symmetric. b1 Numeric vector giving number vertices group first sample. sum vector must match number vertices. p2 matrix giving Bernoulli rates 2nd sample (default: 1st sample). KxK matrix, K number groups. probability creating edge vertices groups j given element (,j). undirected graphs, matrix must symmetric. b2 Numeric vector giving number vertices group second sample (default: 1st sample). sum vector must match number vertices. seed seed random number generator (default: NULL).","code":""},{"path":"https://astamm.github.io/nevada/reference/sample2_sbm.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Two-Sample Stochastic Block Model Generator — sample2_sbm","text":"length-2 list containing two samples stored nvd objects.","code":""},{"path":"https://astamm.github.io/nevada/reference/sample2_sbm.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Two-Sample Stochastic Block Model Generator — sample2_sbm","text":"","code":"n <- 10 p1 <- matrix( data = c(0.1, 0.4, 0.1, 0.4, 0.4, 0.4, 0.1, 0.4, 0.1, 0.1, 0.4, 0.4, 0.4, 0.4, 0.4, 0.4), nrow = 4, ncol = 4, byrow = TRUE ) p2 <- matrix( data = c(0.1, 0.4, 0.4, 0.4, 0.4, 0.4, 0.4, 0.4, 0.4, 0.4, 0.1, 0.1, 0.4, 0.4, 0.1, 0.4), nrow = 4, ncol = 4, byrow = TRUE ) sim <- sample2_sbm(n, 68, p1, c(17, 17, 17, 17), p2, seed = 1234)"},{"path":"https://astamm.github.io/nevada/reference/samplers.html","id":null,"dir":"Reference","previous_headings":"","what":"Graph samplers using edge distributions — samplers","title":"Graph samplers using edge distributions — samplers","text":"collection functions generate random graphs specified edge distribution.","code":""},{"path":"https://astamm.github.io/nevada/reference/samplers.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Graph samplers using edge distributions — samplers","text":"","code":"play_poisson(num_vertices, lambda = 1) rpois_network(n, num_vertices, lambda = 1) play_exponential(num_vertices, rate = 1) rexp_network(n, num_vertices, rate = 1) play_binomial(num_vertices, size = 1, prob = 0.5) rbinom_network(n, num_vertices, size = 1, prob = 0.5)"},{"path":"https://astamm.github.io/nevada/reference/samplers.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Graph samplers using edge distributions — samplers","text":"num_vertices Number vertices. lambda mean parameter Poisson distribution (default: 1). n Sample size. rate rate parameter exponential distribution (default: 1). size number trials binomial distribution (default: 1). prob probability success trial binomial distribution (default: 0.5).","code":""},{"path":"https://astamm.github.io/nevada/reference/samplers.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Graph samplers using edge distributions — samplers","text":"object class nvd containing sample graphs.","code":""},{"path":"https://astamm.github.io/nevada/reference/samplers.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Graph samplers using edge distributions — samplers","text":"","code":"nvd <- rexp_network(10, 68)"},{"path":"https://astamm.github.io/nevada/reference/statistics.html","id":null,"dir":"Reference","previous_headings":"","what":"Test Statistics for Network Populations — statistics","title":"Test Statistics for Network Populations — statistics","text":"collection functions provide statistics testing equality distribution samples networks.","code":""},{"path":"https://astamm.github.io/nevada/reference/statistics.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Test Statistics for Network Populations — statistics","text":"","code":"stat_student_euclidean(d, indices, ...) stat_welch_euclidean(d, indices, ...) stat_original_edge_count(d, indices, edge_count_prep, ...) stat_generalized_edge_count(d, indices, edge_count_prep, ...) stat_weighted_edge_count(d, indices, edge_count_prep, ...)"},{"path":"https://astamm.github.io/nevada/reference/statistics.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Test Statistics for Network Populations — statistics","text":"d Either matrix dimension \\((n1+n2)x(n1+n2)\\) containing distances elements two samples put together (distance-based statistics) concatenation lists matrix representations networks samples 1 2 Euclidean t-Statistics. indices vector dimension \\(n1\\) containing indices elements first sample. ... Extra parameters specific statistics. edge_count_prep list preprocessed data information used edge count statistics produced edge_count_global_variables.","code":""},{"path":"https://astamm.github.io/nevada/reference/statistics.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Test Statistics for Network Populations — statistics","text":"scalar giving value desired test statistic.","code":""},{"path":"https://astamm.github.io/nevada/reference/statistics.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Test Statistics for Network Populations — statistics","text":"details, three main categories statistics: Euclidean t-Statistics: Student stat_student_euclidean version equal variances Welch stat_welch_euclidean version unequal variances, Statistics based similarity graphs: 3 types edge count statistics.","code":""},{"path":"https://astamm.github.io/nevada/reference/statistics.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Test Statistics for Network Populations — statistics","text":"","code":"n1 <- 30L n2 <- 10L gnp_params <- list(n = 24L, p = 1/3) degree_params <- list(out_degree = rep(2, 24L), method = \"configuration\") x <- nvd(sample_size = n1, model = \"gnp\", !!!gnp_params) #> ℹ Calling the `tidygraph::play_gnp()` function with the following arguments: #> • n: 24 #> • p: 0.333333333333333 #> • directed: TRUE #> • loops: FALSE y <- nvd(sample_size = n2, model = \"degree\", !!!degree_params) #> ℹ Calling the `tidygraph::play_degree()` function with the following arguments: #> • out_degree: 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, …, 2, and 2 #> • method: configuration #> • in_degree: NULL r <- repr_nvd(x, y, representation = \"laplacian\") stat_student_euclidean(r, 1:n1) #> [1] 5.790399 stat_welch_euclidean(r, 1:n1) #> [1] 8.347264 d <- dist_nvd(x, y, representation = \"laplacian\", distance = \"frobenius\") ecp <- edge_count_global_variables(d, n1, k = 5L) stat_original_edge_count(d, 1:n1, edge_count_prep = ecp) #> [1] 9.701484 stat_generalized_edge_count(d, 1:n1, edge_count_prep = ecp) #> [1] 218.3131 stat_weighted_edge_count(d, 1:n1, edge_count_prep = ecp) #> [1] 14.7707"},{"path":"https://astamm.github.io/nevada/reference/subgraphs.html","id":null,"dir":"Reference","previous_headings":"","what":"Full, intra and inter subgraph generators — subgraphs","title":"Full, intra and inter subgraph generators — subgraphs","text":"collection functions extracting full, intra inter subgraphs graph given list vertex subsets.","code":""},{"path":"https://astamm.github.io/nevada/reference/subgraphs.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Full, intra and inter subgraph generators — subgraphs","text":"","code":"subgraph_full(g, vids) subgraph_intra(g, vids) subgraph_inter(g, vids)"},{"path":"https://astamm.github.io/nevada/reference/subgraphs.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Full, intra and inter subgraph generators — subgraphs","text":"g igraph object. vids list integer vectors identifying vertex subsets.","code":""},{"path":"https://astamm.github.io/nevada/reference/subgraphs.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Full, intra and inter subgraph generators — subgraphs","text":"igraph object storing subgraph type full, intra inter.","code":""},{"path":"https://astamm.github.io/nevada/reference/subgraphs.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Full, intra and inter subgraph generators — subgraphs","text":"","code":"g <- igraph::make_ring(10) g_full <- subgraph_full (g, list(1:3, 4:5, 8:10)) g_intra <- subgraph_intra(g, list(1:3, 4:5, 8:10)) g_inter <- subgraph_inter(g, list(1:3, 4:5, 8:10))"},{"path":"https://astamm.github.io/nevada/reference/test2_global.html","id":null,"dir":"Reference","previous_headings":"","what":"Global Two-Sample Test for Network-Valued Data — test2_global","title":"Global Two-Sample Test for Network-Valued Data — test2_global","text":"function carries hypothesis test null hypothesis two populations networks share underlying probabilistic distribution alternative hypothesis two populations come different distributions. test performed non-parametric fashion using permutational framework several statistics can used, together several choices network matrix representations distances networks.","code":""},{"path":"https://astamm.github.io/nevada/reference/test2_global.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Global Two-Sample Test for Network-Valued Data — test2_global","text":"","code":"test2_global( x, y, representation = c(\"adjacency\", \"laplacian\", \"modularity\", \"transitivity\"), distance = c(\"frobenius\", \"hamming\", \"spectral\", \"root-euclidean\"), stats = c(\"flipr:t_ip\", \"flipr:f_ip\"), B = 1000L, test = \"exact\", k = 5L, seed = NULL, ... )"},{"path":"https://astamm.github.io/nevada/reference/test2_global.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Global Two-Sample Test for Network-Valued Data — test2_global","text":"x Either object class nvd listing networks sample 1 distance matrix size \\(n_1 + n_2\\). y Either object class nvd listing networks sample 2 integer value specifying size sample 1 integer vector specifying indices observations belonging sample 1. representation string specifying desired type representation, among: \"adjacency\", \"laplacian\" \"modularity\". Defaults \"adjacency\". distance string specifying chosen distance calculating test statistic, among: \"hamming\", \"frobenius\", \"spectral\" \"root-euclidean\". Defaults \"frobenius\". stats character vector specifying chosen test statistic(s), among: \"original_edge_count\", \"generalized_edge_count\", \"weighted_edge_count\", \"student_euclidean\", \"welch_euclidean\" statistics based inter-point distances available flipr package: \"flipr:student_ip\", \"flipr:fisher_ip\", \"flipr:bg_ip\", \"flipr:energy_ip\", \"flipr:cq_ip\". Defaults c(\"flipr:student_ip\", \"flipr:fisher_ip\"). B number permutation tolerance. number lower 1, intended tolerance. Otherwise, intended number required permutations. Defaults 1000L. test character string specifying formula used compute permutation p-value. Choices \"estimate\", \"upper_bound\" \"exact\". Defaults \"exact\" provides exact tests. k integer specifying density minimum spanning tree used edge count statistics. Defaults 5L. seed integer specifying seed random generator result reproducibility. Defaults NULL. ... Extra arguments passed distance function.","code":""},{"path":"https://astamm.github.io/nevada/reference/test2_global.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Global Two-Sample Test for Network-Valued Data — test2_global","text":"list three components: value statistic original two samples, p-value resulting permutation test numeric vector storing values permuted statistics.","code":""},{"path":"https://astamm.github.io/nevada/reference/test2_global.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Global Two-Sample Test for Network-Valued Data — test2_global","text":"","code":"n <- 5L gnp_params <- list(n = 24L, p = 1/3) degree_params <- list(out_degree = rep(2, 24L), method = \"configuration\") # Two different models for the two populations x <- nvd(sample_size = n, model = \"gnp\", !!!gnp_params) #> ℹ Calling the `tidygraph::play_gnp()` function with the following arguments: #> • n: 24 #> • p: 0.333333333333333 #> • directed: TRUE #> • loops: FALSE y <- nvd(sample_size = n, model = \"degree\", !!!degree_params) #> ℹ Calling the `tidygraph::play_degree()` function with the following arguments: #> • out_degree: 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, …, 2, and 2 #> • method: configuration #> • in_degree: NULL t1 <- test2_global(x, y, representation = \"modularity\") #> ! Setting the seed for sampling permutations is mandatory for obtaining a continuous p-value function. Using `seed = 1234`. t1$pvalue #> [1] 0.002308242 # Same model for the two populations x <- nvd(sample_size = n, model = \"gnp\", !!!gnp_params) #> ℹ Calling the `tidygraph::play_gnp()` function with the following arguments: #> • n: 24 #> • p: 0.333333333333333 #> • directed: TRUE #> • loops: FALSE y <- nvd(sample_size = n, model = \"gnp\", !!!gnp_params) #> ℹ Calling the `tidygraph::play_gnp()` function with the following arguments: #> • n: 24 #> • p: 0.333333333333333 #> • directed: TRUE #> • loops: FALSE t2 <- test2_global(x, y, representation = \"modularity\") #> ! Setting the seed for sampling permutations is mandatory for obtaining a continuous p-value function. Using `seed = 1234`. t2$pvalue #> [1] 0.8234127"},{"path":"https://astamm.github.io/nevada/reference/test2_local.html","id":null,"dir":"Reference","previous_headings":"","what":"Local Two-Sample Test for Network-Valued Data — test2_local","title":"Local Two-Sample Test for Network-Valued Data — test2_local","text":"Local Two-Sample Test Network-Valued Data","code":""},{"path":"https://astamm.github.io/nevada/reference/test2_local.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Local Two-Sample Test for Network-Valued Data — test2_local","text":"","code":"test2_local( x, y, partition, representation = \"adjacency\", distance = \"frobenius\", stats = c(\"flipr:t_ip\", \"flipr:f_ip\"), B = 1000L, alpha = 0.05, test = \"exact\", k = 5L, seed = NULL, verbose = FALSE )"},{"path":"https://astamm.github.io/nevada/reference/test2_local.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Local Two-Sample Test for Network-Valued Data — test2_local","text":"x Either object class nvd listing networks sample 1 distance matrix size \\(n_1 + n_2\\). y Either object class nvd listing networks sample 2 integer value specifying size sample 1 integer vector specifying indices observations belonging sample 1. partition Either list integer vector specifying vertex memberships partition elements. representation string specifying desired type representation, among: \"adjacency\", \"laplacian\" \"modularity\". Defaults \"adjacency\". distance string specifying chosen distance calculating test statistic, among: \"hamming\", \"frobenius\", \"spectral\" \"root-euclidean\". Defaults \"frobenius\". stats character vector specifying chosen test statistic(s), among: \"original_edge_count\", \"generalized_edge_count\", \"weighted_edge_count\", \"student_euclidean\", \"welch_euclidean\" statistics based inter-point distances available flipr package: \"flipr:student_ip\", \"flipr:fisher_ip\", \"flipr:bg_ip\", \"flipr:energy_ip\", \"flipr:cq_ip\". Defaults c(\"flipr:student_ip\", \"flipr:fisher_ip\"). B number permutation tolerance. number lower 1, intended tolerance. Otherwise, intended number required permutations. Defaults 1000L. alpha Significance level hypothesis testing. set 1, function outputs properly adjusted p-values. lower 1, p-values lower alpha properly adjusted. Defaults 0.05. test character string specifying formula used compute permutation p-value. Choices \"estimate\", \"upper_bound\" \"exact\". Defaults \"exact\" provides exact tests. k integer specifying density minimum spanning tree used edge count statistics. Defaults 5L. seed integer specifying seed random generator result reproducibility. Defaults NULL. verbose Boolean specifying whether information intermediate tests printed process (default: FALSE).","code":""},{"path":"https://astamm.github.io/nevada/reference/test2_local.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Local Two-Sample Test for Network-Valued Data — test2_local","text":"length-2 list reporting adjusted p-values element partition intra- inter-tests.","code":""},{"path":"https://astamm.github.io/nevada/reference/test2_local.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Local Two-Sample Test for Network-Valued Data — test2_local","text":"","code":"n <- 5L p1 <- matrix( data = c(0.1, 0.4, 0.1, 0.4, 0.4, 0.4, 0.1, 0.4, 0.1, 0.1, 0.4, 0.4, 0.4, 0.4, 0.4, 0.4), nrow = 4, ncol = 4, byrow = TRUE ) p2 <- matrix( data = c(0.1, 0.4, 0.4, 0.4, 0.4, 0.4, 0.4, 0.4, 0.4, 0.4, 0.1, 0.1, 0.4, 0.4, 0.1, 0.4), nrow = 4, ncol = 4, byrow = TRUE ) sim <- sample2_sbm(n, 68, p1, c(17, 17, 17, 17), p2, seed = 1234) m <- as.integer(c(rep(1, 17), rep(2, 17), rep(3, 17), rep(4, 17))) test2_local(sim$x, sim$y, m, seed = 1234, alpha = 0.05, B = 19) #> $intra #> # A tibble: 4 × 3 #> E pvalue truncated #> #> 1 P1 0.548 TRUE #> 2 P2 0.548 TRUE #> 3 P3 0.0480 FALSE #> 4 P4 0.548 TRUE #> #> $inter #> # A tibble: 6 × 4 #> E1 E2 pvalue truncated #> #> 1 P1 P2 0.548 TRUE #> 2 P1 P3 0.0480 FALSE #> 3 P1 P4 0.548 TRUE #> 4 P2 P3 0.0480 FALSE #> 5 P2 P4 0.548 TRUE #> 6 P3 P4 0.0480 FALSE #>"},{"path":"https://astamm.github.io/nevada/reference/var2_nvd.html","id":null,"dir":"Reference","previous_headings":"","what":"Fréchet Variance of Network-Valued Data from Inter-Point Distances — var2_nvd","title":"Fréchet Variance of Network-Valued Data from Inter-Point Distances — var2_nvd","text":"function computes Fréchet variance using exclusively inter-point distances. , can accommodate pair representation distance.","code":""},{"path":"https://astamm.github.io/nevada/reference/var2_nvd.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Fréchet Variance of Network-Valued Data from Inter-Point Distances — var2_nvd","text":"","code":"var2_nvd(x, representation = \"adjacency\", distance = \"frobenius\")"},{"path":"https://astamm.github.io/nevada/reference/var2_nvd.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Fréchet Variance of Network-Valued Data from Inter-Point Distances — var2_nvd","text":"x nvd object listing sample networks. representation string specifying graph representation used. Choices adjacency, laplacian, modularity, graphon. Default adjacency. distance string specifying distance used. Possible choices : hamming, frobenius, spectral root-euclidean. Default frobenius.","code":""},{"path":"https://astamm.github.io/nevada/reference/var2_nvd.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Fréchet Variance of Network-Valued Data from Inter-Point Distances — var2_nvd","text":"positive scalar value evaluating variance based inter-point distances.","code":""},{"path":"https://astamm.github.io/nevada/reference/var2_nvd.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Fréchet Variance of Network-Valued Data from Inter-Point Distances — var2_nvd","text":"","code":"params <- list(n = 24L, p = 1/3) x <- nvd(sample_size = 1L, model = \"gnp\", !!!params) #> ℹ Calling the `tidygraph::play_gnp()` function with the following arguments: #> • n: 24 #> • p: 0.333333333333333 #> • directed: TRUE #> • loops: FALSE var2_nvd(x = x, representation = \"graphon\", distance = \"frobenius\") #> [1] NaN"},{"path":"https://astamm.github.io/nevada/reference/var_nvd.html","id":null,"dir":"Reference","previous_headings":"","what":"Fréchet Variance of Network-Valued Data Around a Given Network — var_nvd","title":"Fréchet Variance of Network-Valued Data Around a Given Network — var_nvd","text":"function computes Fréchet variance around specified network observed sample network-valued random variables according specified distance. cases, user willing compute sample variance, case Fréchet variance evaluated w.r.t. sample Fréchet mean. case, important user indicates distance one (s)used separately compute sample Fréchet mean. function can also used function minimized order find Fréchet mean given distance.","code":""},{"path":"https://astamm.github.io/nevada/reference/var_nvd.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Fréchet Variance of Network-Valued Data Around a Given Network — var_nvd","text":"","code":"var_nvd(x, x0, weights = rep(1, length(x)), distance = \"frobenius\")"},{"path":"https://astamm.github.io/nevada/reference/var_nvd.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Fréchet Variance of Network-Valued Data Around a Given Network — var_nvd","text":"x nvd object listing sample networks. x0 network already matrix representation around calculate variance (usually Fréchet mean necessarily). Note chosen matrix representation extracted parameter. weights numeric vector specifying weights observation (default: equally weighted). distance string specifying distance used. Possible choices : hamming, frobenius, spectral root-euclidean. Default frobenius. Fréchet mean used x0 parameter, distance match one used compute mean. currently checked.","code":""},{"path":"https://astamm.github.io/nevada/reference/var_nvd.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Fréchet Variance of Network-Valued Data Around a Given Network — var_nvd","text":"positive scalar value evaluating amount variability sample around specified network.","code":""},{"path":"https://astamm.github.io/nevada/reference/var_nvd.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Fréchet Variance of Network-Valued Data Around a Given Network — var_nvd","text":"","code":"params <- list(n = 24L, p = 1/3) x <- nvd(sample_size = 1L, model = \"gnp\", !!!params) #> ℹ Calling the `tidygraph::play_gnp()` function with the following arguments: #> • n: 24 #> • p: 0.333333333333333 #> • directed: TRUE #> • loops: FALSE m <- mean(x) var_nvd(x = x, x0 = m, distance = \"frobenius\") #> [1] 0"},{"path":[]},{"path":"https://astamm.github.io/nevada/news/index.html","id":"nevada-020","dir":"Changelog","previous_headings":"","what":"nevada 0.2.0","title":"nevada 0.2.0","text":"CRAN release: 2023-09-03 Improved nvd constructor. Updated GHA scripts. Added tSNE UMAP viz. Added support graphs different sizes /unlabeled graphs. Added support distance matrices test functions. Added support parallelization via future framework furrr.","code":""},{"path":"https://astamm.github.io/nevada/news/index.html","id":"nevada-010","dir":"Changelog","previous_headings":"","what":"nevada 0.1.0","title":"nevada 0.1.0","text":"CRAN release: 2021-09-25 Initial release. Added NEWS.md file track changes package.","code":""}] diff --git a/sitemap.xml b/sitemap.xml index 1ddc1e3..be8af3d 100644 --- a/sitemap.xml +++ b/sitemap.xml @@ -18,7 +18,6 @@ https://astamm.github.io/nevada/reference/nevada-package.html https://astamm.github.io/nevada/reference/nvd-plot.html https://astamm.github.io/nevada/reference/nvd.html -https://astamm.github.io/nevada/reference/pipe.html https://astamm.github.io/nevada/reference/power2.html https://astamm.github.io/nevada/reference/push_to_graph_space.html https://astamm.github.io/nevada/reference/repr_nvd.html