A Well-Behaved Alternative to the Modularity Index

1. Introduction. A major thrust in current network research involves the development of algorithms for uncovering clusters in network data. Network data come in the form of a graph G = (V, E) where V is a set of vertices and E is a set of unordered pairs of vertices, called edges. All these algorithms seek to partition the vertices in V into m > 1 subsets within which vertex-vertex connections are dense, but between which such connections are sparse. Social scientists call such subsets groups, but to physicists they are communities and computer scientists label them clusters. But, regardless of the labeling, all these fields are concerned with the same structural form. Here the neutral term cohesive subsets will be used to refer to structures of this sort.