diff --git a/CHANGELOG.md b/CHANGELOG.md
index 6aaf1d96f9de..1355e7102df7 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -47,6 +47,7 @@ The format is based on [Keep a Changelog](http://keepachangelog.com/en/1.0.0/).
 
 ### Changed
 
+- Accelerated `LineGraph` and fixed issue with self-connected inputs ([#10212](https://github.com/pyg-team/pytorch_geometric/pull/10212))
 - Updated cuGraph examples to use buffered sampling which keeps data in memory and is significantly faster than the deprecated buffered sampling ([#10079](https://github.com/pyg-team/pytorch_geometric/pull/10079))
 - Updated Dockerfile to use latest from NVIDIA ([#9794](https://github.com/pyg-team/pytorch_geometric/pull/9794))
 - Dropped Python 3.8 support ([#9696](https://github.com/pyg-team/pytorch_geometric/pull/9606))
diff --git a/torch_geometric/transforms/line_graph.py b/torch_geometric/transforms/line_graph.py
index 0696f22ae486..be97401d1a8c 100644
--- a/torch_geometric/transforms/line_graph.py
+++ b/torch_geometric/transforms/line_graph.py
@@ -4,7 +4,13 @@
 from torch_geometric.data import Data
 from torch_geometric.data.datapipes import functional_transform
 from torch_geometric.transforms import BaseTransform
-from torch_geometric.utils import coalesce, cumsum, remove_self_loops, scatter
+from torch_geometric.utils import (
+    coalesce,
+    cumsum,
+    remove_self_loops,
+    scatter,
+    to_undirected,
+)
 
 
 @functional_transform('line_graph')
@@ -17,12 +23,11 @@ class LineGraph(BaseTransform):
 
         \mathcal{V}^{\prime} &= \mathcal{E}
 
-        \mathcal{E}^{\prime} &= \{ (e_1, e_2) : e_1 \cap e_2 \neq \emptyset \}
+        \mathcal{E}^{\prime} &=
+         \{ (e_1, e_2) : e_1 \cap e_2 \neq \emptyset,\, e_1 \neq e_2 \}
 
     Line-graph node indices are equal to indices in the original graph's
     coalesced :obj:`edge_index`.
-    For undirected graphs, the maximum line-graph node index is
-    :obj:`(data.edge_index.size(1) // 2) - 1`.
 
     New node features are given by old edge attributes.
     For undirected graphs, edge attributes for reciprocal edges
@@ -43,17 +48,23 @@ def forward(self, data: Data) -> Data:
         edge_index, edge_attr = coalesce(edge_index, edge_attr, num_nodes=N)
         row, col = edge_index
 
+        def vector_arange(start: Tensor, step: Tensor) -> Tensor:
+            step_csum = cumsum(step)[:-1]
+            offset = (step_csum - start).repeat_interleave(step)
+            rng = torch.arange(offset.size(0), dtype=torch.long,
+                               device=offset.device)
+            return rng - offset
+
         if self.force_directed or data.is_directed():
             i = torch.arange(row.size(0), dtype=torch.long, device=row.device)
 
             count = scatter(torch.ones_like(row), row, dim=0,
                             dim_size=data.num_nodes, reduce='sum')
             ptr = cumsum(count)
-
-            cols = [i[ptr[col[j]]:ptr[col[j] + 1]] for j in range(col.size(0))]
-            rows = [row.new_full((c.numel(), ), j) for j, c in enumerate(cols)]
-
-            row, col = torch.cat(rows, dim=0), torch.cat(cols, dim=0)
+            col_count = count[col]
+            row = i.repeat_interleave(col_count)
+            col_index = vector_arange(ptr[col], col_count)
+            col = i[col_index]
 
             data.edge_index = torch.stack([row, col], dim=0)
             data.x = data.edge_attr
@@ -61,39 +72,31 @@ def forward(self, data: Data) -> Data:
 
         else:
             # Compute node indices.
-            mask = row < col
-            row, col = row[mask], col[mask]
-            i = torch.arange(row.size(0), dtype=torch.long, device=row.device)
-
-            (row, col), i = coalesce(
-                torch.stack([
-                    torch.cat([row, col], dim=0),
-                    torch.cat([col, row], dim=0)
-                ], dim=0),
-                torch.cat([i, i], dim=0),
-                N,
-            )
+            mask = row <= col
+            edge_index = edge_index[:, mask]
+            N = edge_index.size(1)
+            i = torch.arange(N, dtype=torch.long, device=row.device)
+            (row, col), i = to_undirected(edge_index, i, num_nodes=N,
+                                          reduce='min')
 
             # Compute new edge indices according to `i`.
             count = scatter(torch.ones_like(row), row, dim=0,
                             dim_size=data.num_nodes, reduce='sum')
-            joints = list(torch.split(i, count.tolist()))
-
-            def generate_grid(x: Tensor) -> Tensor:
-                row = x.view(-1, 1).repeat(1, x.numel()).view(-1)
-                col = x.repeat(x.numel())
-                return torch.stack([row, col], dim=0)
+            ptr = cumsum(count)
+            row = i.repeat_interleave(count[row])
+            count_rep = count.repeat_interleave(count)
+            col_index = vector_arange(ptr[:-1].repeat_interleave(count),
+                                      count_rep)
+            col = i[col_index]
 
-            joints = [generate_grid(joint) for joint in joints]
-            joint = torch.cat(joints, dim=1)
-            joint, _ = remove_self_loops(joint)
-            N = row.size(0) // 2
-            joint = coalesce(joint, num_nodes=N)
+            index = torch.stack([row, col], dim=0)
+            index, _ = remove_self_loops(index)
+            index = coalesce(index, num_nodes=N)
 
             if edge_attr is not None:
                 data.x = scatter(edge_attr, i, dim=0, dim_size=N, reduce='sum')
-            data.edge_index = joint
-            data.num_nodes = edge_index.size(1) // 2
+            data.edge_index = index
+            data.num_nodes = N
 
         data.edge_attr = None