Current-Flow Closeness

Current-flow closeness (Brandes and Fleischer 2005), equal to the information centrality of Stephenson and Zelen (1989), replaces the shortest-path distance in closeness by the effective resistance $R_{vw}$ of the network read as an electrical circuit with the edge weights as conductances: $$CFC(v) = \frac{n - 1}{\sum_{w \ne v} R_{vw}}, \qquad R_{vw} = L^{+}_{vv} + L^{+}_{ww} - 2 L^{+}_{vw},$$ with $L^{+}$ the pseudoinverse of the Laplacian.

Usage

centrality_current_flow_closeness(x, ...)

Arguments

x: Network input accepted by centrality.
...: Further arguments to centrality, such as directed and normalized.

Value

A named numeric vector with one score per node, in input node order.

Details

The measure is defined for connected undirected networks. On a disconnected network every score is NA, with a cograph_undefined_measure warning. On a directed network the Laplacian is built from the asymmetric weight matrix, and directed = FALSE gives the undirected reading. Edge weights are conductances, and weighted = FALSE gives every edge conductance one.

References

Stephenson, K., & Zelen, M. (1989). Rethinking centrality: Methods and examples. Social Networks, 11(1), 1-37. doi:10.1016/0378-8733(89)90016-6 .

Brandes, U., & Fleischer, D. (2005). Centrality measures based on current flow. In STACS 2005, Lecture Notes in Computer Science, 3404 (pp. 533-544). Springer. doi:10.1007/978-3-540-31856-9_44 .

Examples

centrality_current_flow_closeness(regulation_net, directed = FALSE)
#>    Explore       Plan    Monitor      Adapt    Reflect    Discuss Synthesize 
#>  0.6867920  0.7624105  0.7611862  0.7931430  0.6568402  0.7329435  0.4833969 
#>   Evaluate     Create      Share 
#>  0.7485930  0.7090881  0.7652549