networkx.algorithms.edge_betweenness_centrality¶

networkx.algorithms.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 [R655].

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

If None, all edge weights are considered equal. Otherwise holds the name of the edge attribute used as weight.

Returns:

edges : dictionary

Dictionary of edges with betweenness centrality as the value.