networkx.algorithms.centrality.edge_current_flow_betweenness_centrality

networkx.algorithms.centrality.edge_current_flow_betweenness_centrality(G, normalized=True, weight='weight')

Compute current-flow betweenness centrality for edges.

Current-flow betweenness centrality uses an electrical current model for information spreading in contrast to betweenness centrality which uses shortest paths.

Current-flow betweenness centrality is also known as random-walk betweenness centrality [R95].

Parameters :

G : graph

A networkx graph

normalized : bool, optional (default=True)

If True the betweenness values are normalized by b=b/(n-1)(n-2) where n is the number of nodes in G.

weight : string or None, optional (default=’weight’)

Key for edge data used as the edge weight. If None, then use 1 as each edge weight.

Returns :

nodes : dictionary

Dictionary of edge tuples with betweenness centrality as the value.

See also

betweenness_centrality, edge_betweenness_centrality, current_flow_betweenness_centrality

Notes

The algorithm is from Brandes [R94].

If the edges have a ‘weight’ attribute they will be used as weights in this algorithm. Unspecified weights are set to 1.

References

[R94]

(1, 2) Centrality Measures Based on Current Flow. Ulrik Brandes and Daniel Fleischer, Proc. 22nd Symp. Theoretical Aspects of Computer Science (STACS ‘05). LNCS 3404, pp. 533-544. Springer-Verlag, 2005. http://www.inf.uni-konstanz.de/algo/publications/bf-cmbcf-05.pdf

[R95]

(1, 2) A measure of betweenness centrality based on random walks, M. E. J. Newman, Social Networks 27, 39-54 (2005).