# Current-Flow Closeness Centrality

#### Definition

The closeness index based on shortest paths can also be transformed to a measure based on electrical current. For the electrical current model set forth in [BRANDES, U. 2005], Brandes et al. developed an alternative measure of the distance between two vertices s and t, which is defined as the difference of their electrical potentials. Current-flow closeness centrality is defined by
where (n−1) is a normalizing factor, p

Brandes and Fleischer showed that current-flow closeness centrality is equivalent to information centrality [BRANDES, U. 2005].

Li, H., Peng, R., Shan, L., Yi, Y. and Zhang, Z., 2019, May. Current flow group closeness centrality for complex networks?. In The World Wide Web Conference (pp. 961-971).

_{st}(s) is the absolute electrical potential of vertex s based on the electrical current supply from vertex s to vertex t, and p_{st}(s) − p_{st}(t) corresponds to the effective resistance typically measured as voltage, which can be interpreted as an alternative measure of distance between s and t.Brandes and Fleischer showed that current-flow closeness centrality is equivalent to information centrality [BRANDES, U. 2005].

**See Information Centrality****Current flow group closeness centrality**Li, H., Peng, R., Shan, L., Yi, Y. and Zhang, Z., 2019, May. Current flow group closeness centrality for complex networks?. In The World Wide Web Conference (pp. 961-971).

#### Requirements

Require undirected, connected and loop free network.

#### Software

#### References

- BRANDES, U. & FLEISCHER, D. 2005. Centrality measures based on current flow, Springer.