Betweenness Centrality

Betweenness centrality is a measure from graph theory that scores a node by how often it falls along the shortest paths that connect other pairs of nodes in the graph. For a node v, its score adds up, over every pair of other nodes s and t, the fraction of all shortest paths between s and t that pass through v. This raw score can be rescaled to fall between zero and one by dividing by the number of possible node pairs, adjusted depending on whether the graph edges point in a direction or not. Although the general idea of betweenness had been used informally before, Linton Freeman gave it its first formal definition in 1977, and the measure is now applied across networks of many kinds, including telecommunications, social networks, biology and transport systems.