networkx.algorithms.centrality.edge_betweenness_centrality_subset¶

edge_betweenness_centrality_subset(G, sources, targets, normalized=False, weight=None)[source]¶

Compute betweenness centrality for edges for a subset of nodes.

\[c_B(v) =\sum_{s\in S,t \in T} \frac{\sigma(s, t|e)}{\sigma(s, t)}\]

where \(S\) is the set of sources, \(T\) is the set of targets, \(\sigma(s, t)\) 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.
sources (list of nodes) – Nodes to use as sources for shortest paths in betweenness
targets (list of nodes) – Nodes to use as targets for shortest paths in betweenness
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.

Returns

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

Return type

dictionary