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betweenness_centrality(G, nodes)

Betweenness centrality of a node :None:None:`v` is the sum of the fraction of all-pairs shortest paths that pass through :None:None:`v`.

Values of betweenness are normalized by the maximum possible value which for bipartite graphs is limited by the relative size of the two node sets .

Let n be the number of nodes in the node set :None:None:`U` and :None:None:`m` be the number of nodes in the node set :None:None:`V`, then nodes in :None:None:`U` are normalized by dividing by

$$\frac{1}{2} [m^2 (s + 1)^2 + m (s + 1)(2t - s - 1) - t (2s - t + 3)] ,$$

where

$$s = (n - 1) \div m , t = (n - 1) \mod m ,$$

and nodes in :None:None:`V` are normalized by dividing by

$$\frac{1}{2} [n^2 (p + 1)^2 + n (p + 1)(2r - p - 1) - r (2p - r + 3)] ,$$

where,

$$p = (m - 1) \div n , r = (m - 1) \mod n .$$

Notes

The nodes input parameter must contain all nodes in one bipartite node set, but the dictionary returned contains all nodes from both node sets. See bipartite documentation <networkx.algorithms.bipartite> for further details on how bipartite graphs are handled in NetworkX.

Parameters

G : graph: A bipartite graph
nodes : list or container: Container with all nodes in one bipartite node set.

Returns

betweenness : dictionary: Dictionary keyed by node with bipartite betweenness centrality as the value.

Compute betweenness centrality for nodes in a bipartite network.

Examples

See :

Back References

The following pages refer to to this document either explicitly or contain code examples using this.

networkx.algorithms.bipartite.centrality.closeness_centrality networkx.algorithms.bipartite.centrality.degree_centrality

Local connectivity graph

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