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betweenness_centrality¶

betweenness_centrality
(G, nodes)[source]¶ Compute betweenness centrality for nodes in a bipartite network.
Betweenness centrality of a node is the sum of the fraction of allpairs shortest paths that pass through .
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 [1].
Let be the number of nodes in the node set and be the number of nodes in the node set , then nodes in are normalized by dividing by
where
and nodes in are normalized by dividing by
where,
Parameters:  G (graph) – A bipartite graph
 nodes (list or container) – Container with all nodes in one bipartite node set.
Returns: betweenness – Dictionary keyed by node with bipartite betweenness centrality as the value.
Return type: dictionary
See also
degree_centrality()
,closeness_centrality()
,sets()
,is_bipartite()
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.
References
[1] Borgatti, S.P. and Halgin, D. In press. “Analyzing Affiliation Networks”. In Carrington, P. and Scott, J. (eds) The Sage Handbook of Social Network Analysis. Sage Publications. http://www.steveborgatti.com/papers/bhaffiliations.pdf