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 [R118].
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
nodes : list or container


Returns :  betweenness : 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
[R118]  (1, 2) 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 