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# 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].

_{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**#### Requirements

Require undirected, connected and loop free network.

#### Software

#### References

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