Bug: ZeroDivisionError when graph has zero-weight edges

[aryantusharr]

Description

The best_partition() and modularity() functions crash with ZeroDivisionError when the graph contains edges with zero weight. This is an edge case that should be handled gracefully.

Steps to reproduce

import networkx as nx
from community import best_partition, modularity

# Create a graph with zero-weight edges
G = nx.Graph()
G.add_weighted_edges_from([(0, 1, 0.0), (1, 2, 0.0)])

# This crashes with ZeroDivisionError:
partition = best_partition(G)
q = modularity(partition, G, weight='weight')

Expected behavior

Zero-weight edges represent "no connection" and should either:

1. Be skipped/ignored during the algorithm execution, OR
2. Return a meaningful error message instead of crashing

The function should not raise an unhandled ZeroDivisionError.

Root cause

The modularity calculation in the algorithm divides by the edge weight without first checking whether the weight is zero.

Environment

• python-louvain: 0.16
• networkx: 3.6.1
• Python: 3.14.5

[aryantusharr]

@taynaud I would like to work on this issue and submit a fix. I've identified the root cause (division by zero in the modularity calculation when edges have zero weight) and I'm ready to implement a solution.