Current-Flow Closeness Centrality

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_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

Require undirected, connected and loop free network.

• CentiBiN
  http://centibin.ipk-gatersleben.de/
• CentiLib
  http://centilib.ipk-gatersleben.de/
• NetworkX
  https://networkx.github.io/
• RINalyzer
  http://rinalyzer.de/

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