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Betweenness centrality is a metric that seeks to quantify a sense of theimportance of a vertex in a network graph in terms of its "control" on thedistribution of information along geodesic paths throughout that network. Thisquantity however does not capture how different vertices participate togetherin such control. In order to allow for the uncovering of finer details in thisregard, we introduce here an extension of betweenness centrality to pairs ofvertices, which we term co-betweenness, that provides the basis for quantifyingvarious analogous pairwise notions of importance and control. Morespecifically, we motivate and define a precise notion of co-betweenness, wepresent an efficient algorithm for its computation, extending the algorithm ofBrandes in a natural manner, and we illustrate the utilization of thisco-betweenness on a handful of different communication networks. From thesereal-world examples, we show that the co-betweenness allows one to identifycertain vertices which are not the most central vertices but which,nevertheless, act as important actors in the relaying and dispatching ofinformation in the network.

Co-Betweenness: A Pairwise Notion of Centrality