networkx.algorithms.centrality.current_flow_closeness_centrality

current_flow_closeness_centrality(G, weight=None, dtype=<class 'float'>, solver='lu')[source]

Compute current-flow closeness centrality for nodes.

Current-flow closeness centrality is variant of closeness centrality based on effective resistance between nodes in a network. This metric is also known as information centrality.

Parameters

  • G (graph) – A NetworkX graph.

  • weight (None or string, optional (default=None)) – If None, all edge weights are considered equal. Otherwise holds the name of the edge attribute used as weight.

  • dtype (data type (default=float)) – Default data type for internal matrices. Set to np.float32 for lower memory consumption.

  • solver (string (default=’lu’)) – Type of linear solver to use for computing the flow matrix. Options are “full” (uses most memory), “lu” (recommended), and “cg” (uses least memory).

Returns

nodes – Dictionary of nodes with current flow closeness centrality as the value.

Return type

dictionary

See also

closeness_centrality()

Notes

The algorithm is from Brandes 1.

See also 2 for the original definition of information centrality.

References

1

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

2

Karen Stephenson and Marvin Zelen: Rethinking centrality: Methods and examples. Social Networks 11(1):1-37, 1989. https://doi.org/10.1016/0378-8733(89)90016-6