networkx.edge_betweenness_centrality_subset¶

networkx.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 [R898].

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

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.