Fix all_node_cuts output for complete graphs (networkx#6558)

* Fix for complete graphs case in all_node_cuts

* Check node_connectivty in complete graph

* test for broken cuts. add fix

---------

Co-authored-by: Dan Schult <dschult@colgate.edu>

networkx/algorithms/connectivity/kcutsets.py

@@ -93,10 +93,11 @@ def all_node_cuts(G, k=None, flow_func=None):
 
     # Address some corner cases first.
     # For complete Graphs
+
     if nx.density(G) == 1:
-        for cut_set in combinations(G, len(G) - 1):
-            yield set(cut_set)
+        yield from ()
         return
+
     # Initialize data structures.
     # Keep track of the cuts already computed so we do not repeat them.
     seen = []
@@ -130,7 +131,7 @@ def all_node_cuts(G, k=None, flow_func=None):
     for x in X:
         # step 3: Compute local connectivity flow of x with all other
         # non adjacent nodes in G
-        non_adjacent = set(G) - X - set(G[x])
+        non_adjacent = set(G) - {x} - set(G[x])
         for v in non_adjacent:
             # step 4: compute maximum flow in an Even-Tarjan reduction H of G
             # and step 5: build the associated residual network R

networkx/algorithms/connectivity/tests/test_kcutsets.py

@@ -259,8 +259,15 @@ def test_cycle_graph():
 
 def test_complete_graph():
     G = nx.complete_graph(5)
-    solution = [{0, 1, 2, 3}, {0, 1, 2, 4}, {0, 1, 3, 4}, {0, 2, 3, 4}, {1, 2, 3, 4}]
-    cuts = list(nx.all_node_cuts(G))
-    assert len(solution) == len(cuts)
-    for cut in cuts:
-        assert cut in solution
+    assert nx.node_connectivity(G) == 4
+    assert list(nx.all_node_cuts(G)) == []
+
+
+def test_all_node_cuts_simple_case():
+    G = nx.complete_graph(5)
+    G.remove_edges_from([(0, 1), (3, 4)])
+    expected = [{0, 1, 2}, {2, 3, 4}]
+    actual = list(nx.all_node_cuts(G))
+    assert len(actual) == len(expected)
+    for cut in actual:
+        assert cut in expected