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:

Ggraph: 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
normalizedbool, 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.
weightNone or string, optional (default=None): If None, all edge weights are considered equal. Otherwise holds the name of the edge attribute used as weight. Weights are used to calculate weighted shortest paths, so they are interpreted as distances.

Returns:

nodesdictionary: Dictionary of nodes with betweenness centrality as the value.