trophic_levels now checks for paths from each node to a basal node

[Aditya-Shandilya1182]

Fixes #6899

[Aditya-Shandilya1182]

I added the function bfs_reachable_from_basal to perform BFS and determine nodes reachable from basal nodes.

• Initialized visited and reachable_nodes sets to track visited nodes and reachable nodes respectively.
• Iterated over basal nodes and used BFS to explore all reachable nodes, adding them to the reachable_nodes set.
• Raised nx.NetworkXError if no basal nodes are present, indicating that trophic levels are not defined.
• Checked if all nodes in the graph are reachable from the basal nodes, raising nx.NetworkXError if not.

Following code was used to check the proper functioning of the feature.

edges = [(0, 5), (0, 3), (0, 33), (3, 2), (3, 24), (3, 32), (33, 1), (33, 10), (2, 3), (2, 16), (1, 33), (10, 16), (16, 4), (16, 9), (18, 11), (11, 5), (11, 21), (4, 2), (4, 33), (9, 16), (9, 26), (9, 17), (26, 19), (17, 10), (19, 10), (19, 9), (19, 7), (19, 0)]
G = nx.DiGraph(edges)
res = nx.trophic_levels(G)
print(res[0])

Result before changes:

Result after changes:

[Aditya-Shandilya1182]

This code is written to address issue #6899.

[dschult]

Thanks for this!
I think the bulk of this could call the existing nx.bfs_layers function which takes a parameter for multiple source nodes.

See below.

[rossbar]

At first glance this seems to be on the right track, thanks! This should also have some test cases to demonstrate the changed/fixed behavior in trophic_levels!

[rossbar]

I'd vote to use this directly on L59 and do away with the extra function definition - eliminating indirection makes the code much easier to follow IMO!

[Aditya-Shandilya1182]

I will try to add the test cases.

[dschult]

I include a comment with the term

Fixes #6899

so that merging this PR automatically closes that issue.
More on linking a Pr to an Issue
[Edit: -- oops! that phrase has to be in the original post. I added it there so they are connected.]

[dschult]

I think the tests actually passed -- it was a red X because one test got canceled, but rerunning it allowed it to pass.

A second test could be a graph that works plus an isolated node. That will trigger the other exception added in this PR.

[eriknw]

This looks like a reasonable approach. The latest dev version of np.linalg.inv says this:

If a is detected to be singular, a LinAlgError is raised. If a is ill-conditioned, a LinAlgError may or may not be raised, and results may be inaccurate due to floating-point errors.

Should a more clear error message be given for the null graph? nx.trophic_levels(nx.DiGraph()) currently raises NetworkXError: Graph has no nodes or edges

[Aditya-Shandilya1182]

I think the tests actually passed -- it was a red X because one test got canceled, but rerunning it allowed it to pass.

A second test could be a graph that works plus an isolated node. That will trigger the other exception added in this PR.

Are you referring to the test case I added and then removed?

[dschult]

Yes -- I was referring to the test added and then removed. That tested the "no basal nodes" exception.

[Aditya-Shandilya1182]

Should I add it again then?

[dschult]

Yes -- could you add it again, and a test for a network that should work, but with an added isolated node so that it doesn't work -- and raises an exception from the 2nd code-check. Does this make sense?

[Aditya-Shandilya1182]

I tried adding a test for isolated nodes. But the test failed. Should I add a condition to handle isolated nodes? Or is there something I am missing here?

Test:

def test_trophic_levels_with_isolated_node():
    G = nx.DiGraph()
    # Adding edges to create a graph with a basal node
    edges = [(0, 1), (1, 2), (2, 3)]
    G.add_edges_from(edges)
    
    # Adding an isolated node
    G.add_node(4)
    print(G.nodes)
    
    with pytest.raises(nx.NetworkXError):
        nx.trophic_levels(G)