Enter search terms or a module, class or function name.
Compute the shortest-path betweenness centrality for nodes.
Betweenness centrality of a node
System Message: WARNING/2 (v)
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System Message: WARNING/2 (V)
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k : int, optional (default=None)
normalized : bool, optional
weight : None or string, optional
endpoints : bool, optional
|
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Returns : | nodes : dictionary
|
See also
Notes
The algorithm is from Ulrik Brandes [R130]. See [R131] for details on algorithms for variations and related metrics.
For approximate betweenness calculations set k=#samples to use k nodes (“pivots”) to estimate the betweenness values. For an estimate of the number of pivots needed see [R132].
For weighted graphs the edge weights must be greater than zero. Zero edge weights can produce an infinite number of equal length paths between pairs of nodes.
References
[R130] | (1, 2) A Faster Algorithm for Betweenness Centrality. Ulrik Brandes, Journal of Mathematical Sociology 25(2):163-177, 2001. http://www.inf.uni-konstanz.de/algo/publications/b-fabc-01.pdf |
[R131] | (1, 2, 3) Ulrik Brandes: On Variants of Shortest-Path Betweenness Centrality and their Generic Computation. Social Networks 30(2):136-145, 2008. http://www.inf.uni-konstanz.de/algo/publications/b-vspbc-08.pdf |
[R132] | (1, 2) Ulrik Brandes and Christian Pich: Centrality Estimation in Large Networks. International Journal of Bifurcation and Chaos 17(7):2303-2318, 2007. http://www.inf.uni-konstanz.de/algo/publications/bp-celn-06.pdf |