Warning

This documents an unmaintained version of NetworkX. Please upgrade to a maintained version and see the current NetworkX documentation.

# networkx.algorithms.centrality.edge_betweenness_centrality¶

edge_betweenness_centrality(G, k=None, normalized=True, weight=None, seed=None)[source]

Compute betweenness centrality for edges.

Betweenness centrality of an edge $$e$$ is the sum of the fraction of all-pairs shortest paths that pass through $$e$$

$c_B(e) =\sum_{s,t \in V} \frac{\sigma(s, t|e)}{\sigma(s, t)}$

where $$V$$ is the set of nodes, $$\sigma(s, t)$$ is the number of shortest $$(s, t)$$-paths, and $$\sigma(s, t|e)$$ is the number of those paths passing through edge $$e$$ [2].

Parameters: G (graph) – A NetworkX graph. k (int, optional (default=None)) – If k is not None use k node samples to estimate betweenness. The value of k <= n where n is the number of nodes in the graph. Higher values give better approximation. normalized (bool, optional) – If True the betweenness values are normalized by $$2/(n(n-1))$$ for graphs, and $$1/(n(n-1))$$ for directed graphs where $$n$$ is the number of nodes in G. weight (None or string, optional (default=None)) – If None, all edge weights are considered equal. Otherwise holds the name of the edge attribute used as weight. seed (integer, random_state, or None (default)) – Indicator of random number generation state. See Randomness. Note that this is only used if k is not None. edges – Dictionary of edges with betweenness centrality as the value. dictionary

betweenness_centrality(), edge_load()