  Betweenness centrality is a metric that seeks to quantify a sense of the
importance of a vertex in a network graph in terms of its "control" on the
distribution of information along geodesic paths throughout that network. This
quantity however does not capture how different vertices participate together
in such control. In order to allow for the uncovering of finer details in this
regard, we introduce here an extension of betweenness centrality to pairs of
vertices, which we term co-betweenness, that provides the basis for quantifying
various analogous pairwise notions of importance and control. More
specifically, we motivate and define a precise notion of co-betweenness, we
present an efficient algorithm for its computation, extending the algorithm of
Brandes in a natural manner, and we illustrate the utilization of this
co-betweenness on a handful of different communication networks. From these
real-world examples, we show that the co-betweenness allows one to identify
certain vertices which are not the most central vertices but which,
nevertheless, act as important actors in the relaying and dispatching of
information in the network.
