Fixed test for average shortest path in the case of directed graphs (#6003)

* Fixed test for average shortest path in the case of directed graphs

* Fixed order

* Update networkx/algorithms/shortest_paths/tests/test_generic.py

Co-authored-by: Ross Barnowski <rossbar@berkeley.edu>

* Release bullet; added versionchanged

* Add brief description to versionchanged directive.

* Fixed definition

* Using \substack

Co-authored-by: Ross Barnowski <rossbar@berkeley.edu>

3 files changed, 20 insertions, 8 deletions

diff --git a/doc/release/release_dev.rst b/doc/release/release_dev.rst
index faad122b..4c72240e 100644
--- a/doc/release/release_dev.rst
+++ b/doc/release/release_dev.rst
@@ -61,6 +61,10 @@ Improvements
   ``is_path`` used to raise a `KeyError` when the ``path`` argument contained
   a node that was not in the Graph. The behavior has been updated so that
   ``is_path`` returns `False` in this case rather than raising the exception.
+- [`#6003 <https://github.com/networkx/networkx/pull/6003>`_]
+  ``avg_shortest_path_length`` now raises an exception if the provided
+  graph is directed but not strongly connected. The previous test (weak
+  connecting) was wrong; in that case, the returned value was nonsensical.
 
 API Changes
 -----------
diff --git a/networkx/algorithms/shortest_paths/generic.py b/networkx/algorithms/shortest_paths/generic.py
index 129f7417..fdced25d 100644
--- a/networkx/algorithms/shortest_paths/generic.py
+++ b/networkx/algorithms/shortest_paths/generic.py
@@ -320,12 +320,16 @@ def average_shortest_path_length(G, weight=None, method=None):
 
     .. math::
 
-       a =\sum_{s,t \in V} \frac{d(s, t)}{n(n-1)}
+       a =\sum_{\substack{s,t \in V \\ s\neq t}} \frac{d(s, t)}{n(n-1)}
 
     where `V` is the set of nodes in `G`,
     `d(s, t)` is the shortest path from `s` to `t`,
     and `n` is the number of nodes in `G`.
 
+    .. versionchanged:: 3.0
+       An exception is raised for directed graphs that are not strongly
+       connected.
+
     Parameters
     ----------
     G : NetworkX graph
@@ -354,7 +358,7 @@ def average_shortest_path_length(G, weight=None, method=None):
         If `G` is the null graph (that is, the graph on zero nodes).
 
     NetworkXError
-        If `G` is not connected (or not weakly connected, in the case
+        If `G` is not connected (or not strongly connected, in the case
         of a directed graph).
 
     ValueError
@@ -397,9 +401,10 @@ def average_shortest_path_length(G, weight=None, method=None):
     # For the special case of the trivial graph, return zero immediately.
     if n == 1:
         return 0
-    # Shortest path length is undefined if the graph is disconnected.
-    if G.is_directed() and not nx.is_weakly_connected(G):
-        raise nx.NetworkXError("Graph is not weakly connected.")
+    # Shortest path length is undefined if the graph is not strongly connected.
+    if G.is_directed() and not nx.is_strongly_connected(G):
+        raise nx.NetworkXError("Graph is not strongly connected.")
+    # Shortest path length is undefined if the graph is not connected.
     if not G.is_directed() and not nx.is_connected(G):
         raise nx.NetworkXError("Graph is not connected.")
 
diff --git a/networkx/algorithms/shortest_paths/tests/test_generic.py b/networkx/algorithms/shortest_paths/tests/test_generic.py
index 093fd9c7..91b0e309 100644
--- a/networkx/algorithms/shortest_paths/tests/test_generic.py
+++ b/networkx/algorithms/shortest_paths/tests/test_generic.py
@@ -324,13 +324,16 @@ class TestAverageShortestPathLength:
         )
         assert ans == pytest.approx(4, abs=1e-7)
 
-    def test_disconnected(self):
+    def test_directed_not_strongly_connected(self):
+        G = nx.DiGraph([(0, 1)])
+        with pytest.raises(nx.NetworkXError, match="Graph is not strongly connected"):
+            nx.average_shortest_path_length(G)
+
+    def test_undirected_not_connected(self):
         g = nx.Graph()
         g.add_nodes_from(range(3))
         g.add_edge(0, 1)
         pytest.raises(nx.NetworkXError, nx.average_shortest_path_length, g)
-        g = g.to_directed()
-        pytest.raises(nx.NetworkXError, nx.average_shortest_path_length, g)
 
     def test_trivial_graph(self):
         """Tests that the trivial graph has average path length zero,