Repository: networkx/networkx

Issue:
could_be_isomorphic returns False for an isomorphic graph on 3.2
<!-- If you have a general question about NetworkX, please use the discussions tab to create a new discussion -->

<!--- Provide a general summary of the issue in the Title above -->

### Current Behavior

We have noticed a new failure on downstream testing using isomorphic checks when updating to networkx 3.2. We know that the graph we check is isomorphic, yet `nx.could_be_isomorphic` started returning `False`, which I believe is a regression in the latest release.

<!--- Tell us what happens instead of the expected behavior -->

### Expected Behavior

`nx.could_be_isomorphic` should return `True` for an isomorphic graph

<!--- Tell us what should happen -->

### Steps to Reproduce

```py
import networkx as nx

left = nx.read_gexf("left.gexf")
right = nx.read_gexf("right.gexf")
assert nx.is_isomorphic(left, right)
nx.could_be_isomorphic(left, right) # should be True but is False
```
<!--- Provide a minimal example that reproduces the bug -->

### Environment

<!--- Please provide details about your local environment -->

Python version: 3.9 - 3.12
NetworkX version: 3.2

### Additional context

<!--- Add any other context about the problem here, screenshots, etc. -->

The gefx files:

[Archive.zip](https://github.com/networkx/networkx/files/13061063/Archive.zip)




Discussion:
Thanks for reporting this!!
Is the `nxleft` and `nxright` in your example code (in the assert statement) supposed to be `left` and `right`?

Also, can you describe how you know these are isomorphic graphs?
Do you have the isomorphism? Or is that result based on previous networkx results?  
> Is the nxleft and nxright in your example code (in the assert statement) supposed to be left and right?

Yes, sorry!

Both left and right come from the same edge list, only ids are remapped. It is the same graph and it is isomorphic as proved by the assertion. Something has changed in the `could_be_isomorphic` function that it started returning False (which is wrong). 
I can verify that `could_be_isomorphic` and `fast_could_be_isomorphic` return apparently false results for this case. And I've traced it to the computation of `triangles`. One node is only connected to itself by a self-loop (node "46" in right which is isomorphic to node "8" in left).  Those nodes are getting a different number of triangles in the two graphs when using `nx.triangles`.  The self-loop is the only edge involving those nodes in the graphs. 

`nx.triangles was changed 3 months ago in #6258 so I think an error was introduced there -- something about self-loops but even worse, something that counts the triangles differently depending on relabeling the nodes.


Resolving patch:
diff --git a/networkx/algorithms/cluster.py b/networkx/algorithms/cluster.py
--- a/networkx/algorithms/cluster.py
+++ b/networkx/algorithms/cluster.py
@@ -72,7 +72,7 @@ def triangles(G, nodes=None):
     # iterate over the nodes in a graph
     for node, neighbors in G.adjacency():
         later_neighbors[node] = {
-            n for n in neighbors if n not in later_neighbors and n is not node
+            n for n in neighbors if n not in later_neighbors and n != node
         }
 
     # instantiate Counter for each node to include isolated nodes
diff --git a/networkx/algorithms/similarity.py b/networkx/algorithms/similarity.py
--- a/networkx/algorithms/similarity.py
+++ b/networkx/algorithms/similarity.py
@@ -1363,7 +1363,7 @@ def sim(u, v):
 
     for its in range(max_iterations):
         oldsim = newsim
-        newsim = {u: {v: sim(u, v) if u is not v else 1 for v in G} for u in G}
+        newsim = {u: {v: sim(u, v) if u != v else 1 for v in G} for u in G}
         is_close = all(
             all(
                 abs(newsim[u][v] - old) <= tolerance * (1 + abs(old))


Test patch: