current_flow_closeness_centrality

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

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:

Ggraph

A NetworkX graph.

weightNone or string, optional (default=None)

If None, all edge weights are considered equal. Otherwise holds the name of the edge attribute used as weight. The weight reflects the capacity or the strength of the edge.

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:

nodesdictionary

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

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. https://doi.org/10.1007/978-3-540-31856-9_44

[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