Fix edge_insensitive homophily measure (#4152)

* Fix torch_geometric/utils/homophily.py: mean -> sum & div_by_c-1

* Fix torch_geometric/utils/homophily: edge_homophily -> h_k

* Fix torch_geometric/utils/homophily.py: batch mode

* fix test

Co-authored-by: Matthias Fey <matthias.fey@tu-dortmund.de>

test/utils/test_homophily.py

@@ -23,6 +23,6 @@ def test_homophily():
     assert homophily(edge_index, y, batch, method).tolist() == [1., 0.]
 
     method = 'edge_insensitive'
-    assert pytest.approx(homophily(edge_index, y, method=method)) == 0.0999999
-    assert pytest.approx(homophily(adj, y, method=method)) == 0.0999999
+    assert pytest.approx(homophily(edge_index, y, method=method)) == 0.1999999
+    assert pytest.approx(homophily(adj, y, method=method)) == 0.1999999
     assert homophily(edge_index, y, batch, method).tolist() == [0., 0.]

torch_geometric/utils/homophily.py

@@ -43,7 +43,7 @@ def homophily(edge_index: Adj, y: Tensor, batch: OptTensor = None,
       and size of each class:
 
       .. math::
-        \frac{1}{C} \sum_{k=1}^{C} \max \left(0, h_k - \frac{|\mathcal{C}_k|}
+        \frac{1}{C-1} \sum_{k=1}^{C} \max \left(0, h_k - \frac{|\mathcal{C}_k|}
         {|\mathcal{V}|} \right),
 
       where :math:`C` denotes the number of classes, :math:`|\mathcal{C}_k|`
@@ -93,6 +93,7 @@ def homophily(edge_index: Adj, y: Tensor, batch: OptTensor = None,
     elif method == 'edge_insensitive':
         assert y.dim() == 1
         num_classes = int(y.max()) + 1
+        assert num_classes >= 2
         batch = torch.zeros_like(y) if batch is None else batch
         num_nodes = degree(batch, dtype=torch.int64)
         num_graphs = num_nodes.numel()
@@ -105,7 +106,8 @@ def homophily(edge_index: Adj, y: Tensor, batch: OptTensor = None,
         counts = counts.view(num_graphs, num_classes)
         proportions = counts / num_nodes.view(-1, 1)
 
-        out = (h - proportions).clamp_(min=0).mean(dim=-1)
+        out = (h - proportions).clamp_(min=0).sum(dim=-1)
+        out /= num_classes - 1
         return out if out.numel() > 1 else float(out)
 
     else: