Fix random_spanning_tree() for single node and empty graphs

networkx/algorithms/tree/mst.py

@@ -897,14 +897,15 @@ def spanning_tree_total_weight(G, weight):
             #    itself.
             if G.number_of_edges() == 1:
                 return G.edges(data=weight).__iter__().__next__()[2]
-            # 2. There are more than two edges in the graph. Then, we can find the
+            # 2. There are no edges or two or more edges in the graph. Then, we find the
             #    total weight of the spanning trees using the formula in the
-            #    reference paper: take the weight of that edge and multiple it by
-            #    the number of spanning trees which have to include that edge. This
+            #    reference paper: take the weight of each edge and multiply it by
+            #    the number of spanning trees which include that edge. This
             #    can be accomplished by contracting the edge and finding the
             #    multiplicative total spanning tree weight if the weight of each edge
             #    is assumed to be 1, which is conveniently built into networkx already,
-            #    by calling total_spanning_tree_weight with weight=None
+            #    by calling total_spanning_tree_weight with weight=None.
+            #    Note that with no edges the returned value is just zero.
             else:
                 total = 0
                 for u, v, w in G.edges(data=weight):
@@ -913,6 +914,10 @@ def spanning_tree_total_weight(G, weight):
                     )
                 return total
 
+    if G.number_of_nodes() < 2:
+        # no edges in the spanning tree
+        return nx.empty_graph(G.nodes)
+
     U = set()
     st_cached_value = 0
     V = set(G.edges())

networkx/algorithms/tree/tests/test_mst.py

@@ -706,3 +706,27 @@ def test_random_spanning_tree_additive_large():
     # Assert that p is greater than the significance level so that we do not
     # reject the null hypothesis
     assert not p < 0.05
+
+
+def test_random_spanning_tree_empty_graph():
+    G = nx.Graph()
+    rst = nx.tree.random_spanning_tree(G)
+    assert len(rst.nodes) == 0
+    assert len(rst.edges) == 0
+
+
+def test_random_spanning_tree_single_node_graph():
+    G = nx.Graph()
+    G.add_node(0)
+    rst = nx.tree.random_spanning_tree(G)
+    assert len(rst.nodes) == 1
+    assert len(rst.edges) == 0
+
+
+def test_random_spanning_tree_single_node_loop():
+    G = nx.Graph()
+    G.add_node(0)
+    G.add_edge(0, 0)
+    rst = nx.tree.random_spanning_tree(G)
+    assert len(rst.nodes) == 1
+    assert len(rst.edges) == 0