Update simple_paths.py: consistent behaviour for `is_simple_path` when path contains nodes not in the graph. (#6272)

* Update simple_paths.py

Current version of `is_simple_path` fails with `KeyError` if the first element of the node list is not in the graph.

* Update simple_paths.py

* Update simple_paths.py

Simplify the test condition. Checking for a single node in the list can be combined with checking for duplicates in the list without meaningful efficiency loss.

* Update test_simple_paths.py

Add the case when the start of the path is a node not in the graph.

* Update simple_paths.py

* Update simple_paths.py

* Update simple_paths.py

* Update simple_paths.py

* Update simple_paths.py

Still need to check the special case of a list with 1 item.

2 files changed, 17 insertions, 3 deletions

diff --git a/networkx/algorithms/simple_paths.py b/networkx/algorithms/simple_paths.py
index d6baa23b..d81d2345 100644
--- a/networkx/algorithms/simple_paths.py
+++ b/networkx/algorithms/simple_paths.py
@@ -72,13 +72,23 @@ def is_simple_path(G, nodes):
     # NetworkXPointlessConcept here.
     if len(nodes) == 0:
         return False
+
     # If the list is a single node, just check that the node is actually
     # in the graph.
     if len(nodes) == 1:
         return nodes[0] in G
-    # Test that no node appears more than once, and that each
-    # adjacent pair of nodes is adjacent.
-    return len(set(nodes)) == len(nodes) and all(v in G[u] for u, v in pairwise(nodes))
+
+    # check that all nodes in the list are in the graph, if at least one
+    # is not in the graph, then this is not a simple path
+    if not all(n in G for n in nodes):
+        return False
+
+    # If the list contains repeated nodes, then it's not a simple path
+    if len(set(nodes)) != len(nodes):
+        return False
+
+    # Test that each adjacent pair of nodes is adjacent.
+    return all(v in G[u] for u, v in pairwise(nodes))
 
 
 def all_simple_paths(G, source, target, cutoff=None):
diff --git a/networkx/algorithms/tests/test_simple_paths.py b/networkx/algorithms/tests/test_simple_paths.py
index 08348b98..c2d4c008 100644
--- a/networkx/algorithms/tests/test_simple_paths.py
+++ b/networkx/algorithms/tests/test_simple_paths.py
@@ -58,6 +58,10 @@ class TestIsSimplePath:
         G = nx.path_graph(2)
         assert not nx.is_simple_path(G, [0, 2])
 
+    def test_missing_starting_node(self):
+        G = nx.path_graph(2)
+        assert not nx.is_simple_path(G, [2, 0])
+
     def test_directed_path(self):
         G = nx.DiGraph([(0, 1), (1, 2)])
         assert nx.is_simple_path(G, [0, 1, 2])