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 all-pairs 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