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