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 \(s\) and \(t\). If \(s = t\), \(\sigma(s, t) = 1\), and if \(v \in \{s, t\}\), \(\sigma(s, t | v) = 0\) [2]. The denominator \(\sigma(s, t)\) is a normalization factor that can be turned off to get the raw path counts.

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 (default=False): If True, the betweenness values are rescaled by dividing by the number of possible \((s, t)\)-pairs in the graph.
weightNone or string, optional (default=None): If None, all edge weights are 1. 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:

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