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Bridgeness CentralityDefinition
In a graph G =(V, E), where V assigns the set of nodes and E the set of links the definition of the Betweenness Centrality (BC) for a node j ∈ V stands as:
where Here the summation runs over any distinct node pairs i and k; σik represents the number of shortest paths between i and k; while σ_{ik}(j) is the number of such shortest paths running through j. Decomposing BC into two parts (righthand side) the first term defines actually the global term, bridgeness centrality, where we consider shortest paths between nodes not in the neighbourhood of j (NG(j)), while the second local term considers the shortest paths starting or ending in the neighbourhood of j. References
