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CurrentFlow Closeness CentralityDefinition
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. Currentflow 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 currentflow closeness centrality is equivalent to information centrality [BRANDES, U. 2005]. See Information Centrality Requirements
Require undirected, connected and loop free network.
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