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.

Returns

edges – Dictionary of edges with betweenness centrality as the value.

Return type

dictionary