networkx.algorithms.centrality.betweenness_centrality_subset¶

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

Compute betweenness centrality for a subset of nodes.

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

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 \(\sigma(s, t|v)\) is the number of those paths passing through some node \(v\) other than \(s, t\). If \(s = t\), \(\sigma(s, t) = 1\), and if \(v \in {s, t}\), \(\sigma(s, t|v) = 0\) 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 \(2/((n-1)(n-2))\) for graphs, and \(1/((n-1)(n-2))\) 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

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

Return type

dictionary