Fix custom weight attribute for Mehlhorn

networkx/algorithms/approximation/steinertree.py

@@ -64,7 +64,7 @@ def _mehlhorn_steiner_tree(G, terminal_nodes, weight):
         if not G_1_prime.has_edge(su, sv):
             G_1_prime.add_edge(su, sv, weight=weight_here)
         else:
-            new_weight = min(weight_here, G_1_prime[su][sv][weight])
+            new_weight = min(weight_here, G_1_prime[su][sv]["weight"])
             G_1_prime.add_edge(su, sv, weight=new_weight)
 
     G_2 = nx.minimum_spanning_edges(G_1_prime, data=True)

networkx/algorithms/approximation/tests/test_steinertree.py

@@ -189,3 +189,22 @@ def test_multigraph_steiner_tree(self):
         for method in self.methods:
             S = steiner_tree(G, terminal_nodes, method=method)
             assert edges_equal(S.edges(data=True, keys=True), expected_edges)
+
+
+@pytest.mark.parametrize("method", ("kou", "mehlhorn"))
+def test_steiner_tree_weight_attribute(method):
+    G = nx.star_graph(4)
+    # Add an edge attribute that is named something other than "weight"
+    nx.set_edge_attributes(G, {e: 10 for e in G.edges}, name="distance")
+    H = nx.approximation.steiner_tree(G, [1, 3], method=method, weight="distance")
+    assert nx.utils.edges_equal(H.edges, [(0, 1), (0, 3)])
+
+
+@pytest.mark.parametrize("method", ("kou", "mehlhorn"))
+def test_steiner_tree_multigraph_weight_attribute(method):
+    G = nx.cycle_graph(3, create_using=nx.MultiGraph)
+    nx.set_edge_attributes(G, {e: 10 for e in G.edges}, name="distance")
+    G.add_edge(2, 0, distance=5)
+    H = nx.approximation.steiner_tree(G, list(G), method=method, weight="distance")
+    assert len(H.edges) == 2 and H.has_edge(2, 0, key=1)
+    assert sum(dist for *_, dist in H.edges(data="distance")) == 15