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networkx.algorithms.centrality.current_flow_closeness_centrality

current_flow_closeness_centrality(G, weight=None, dtype=<type '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