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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

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is the sum of the fraction of all-pairs shortest paths that pass through

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.

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

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be the number of nodes in the node set

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and

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be the number of nodes in the node set

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, then nodes in

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are normalized by dividing by

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where

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and nodes in

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are normalized by dividing by

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where,

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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.

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