ZeroDivisionError in "nx.global_reaching_centrality" and "nx.local_reaching_centrality" caused by the graph contains only one node.

[joyemang33]

Hello! Sorry for bothering you again.
When testing NetworkX, I found a ZeroDivisonError crash in nx.global_reaching_centrality when the input graph only contains one node, with the following message:

File "/home/qiuyang/.local/lib/python3.10/site-packages/networkx/algorithms/centrality/reaching.py", line 196, in local_reaching_centrality
    return (len(paths) - 1) / (len(G) - 1)

I am not sure whether reaching_centrality has a good definition in such cases, but this ZeroDivisonError may not be good to show for users. Could you further help me confirm and investigate it, it would be highly appreciated.

The statement that triggers the exception is here.

Best regards,
Joye

Step to Reproduce

import networkx as nx

G = nx.DiGraph([(1, 1)])
G.add_node(1)
print(nx.global_reaching_centrality(G))
print(nx.local_reaching_centrality(G, v=1))

Result

ZeroDivisionError

Environment

NetworkX 3.1
Python 3.10

[joyemang33]

After the investigation, I found that there are similar issues in nx.flow_hierarchy, non_randomness, approximate_current_flow_betweenness_centrality, edge_current_flow_betweenness_centrality, and current_flow_betweenness_centrality.

I found that Flow Hierarchy has no definition in such graphs, maybe we should return a NetworkX Exception to warn users in such cases. For flow_betweenness_centrality, I am not sure whether we should return a NetworkX Exception or calculate the centrality for such a graph.

import networkx as nx

G = nx.DiGraph()
G.add_node(1)
print(nx.flow_hierarchy(G))

import networkx as nx

G = nx.Graph()
G.add_node(0)
print(nx.current_flow_betweenness_centrality(G))

Result

ZeroDivisionError

Best regards,
Joye

[joyemang33]

PS: HITS also failed in such a graph with the message:

File "/home/qiuyang/.local/lib/python3.10/site-packages/networkx/algorithms/link_analysis/hits_alg.py", line 82, in hits
    _, _, vt = sp.sparse.linalg.svds(A, k=1, maxiter=max_iter, tol=tol)
  File "/home/qiuyang/.local/lib/python3.10/site-packages/scipy/sparse/linalg/_eigen/_svds.py", line 443, in svds
    args = _iv(A, k, ncv, tol, which, v0, maxiter, return_singular_vectors,
  File "/home/qiuyang/.local/lib/python3.10/site-packages/scipy/sparse/linalg/_eigen/_svds.py", line 49, in _iv
    raise ValueError(message)
ValueError: `k` must be an integer satisfying `0 < k < min(A.shape)`.

import networkx as nx

G = nx.DiGraph()
G.add_node(1)
print(nx.hits(G))

Result

Exception has occurred: ValueError

Best regards,
Joye