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Flow Betweenness CentralityDefinition
Unnormalized flow betweenness
Freeman et al. define the raw or unnormalized flow betweenness of a vertex, v ∈ V(G) as: where f(i, j, G) is the maximum flow from i to j within G (under the assumption of infinite vertex capacities, finite edge capacities, and nonsimultaneity of pairwise flows). Intuitively, unnormalized flow betweenness is simply the total maximum flow (aggregated across all pairs of third parties) mediated by v. Normalized flow betweenness Normalize the raw flow betweenness by the total maximum flow among third parties (including v); this leads to the following normalized flow betweenness measure: Variant by Koschutzki et al. where 0/0 flow ratios are treated as 0 (as in shortestpath betweenness). References
