Communities in Graphs

Many applications, like the retrieval of information from the WWW, require or are improved by the detection of sets of closely related vertices in graphs. Depending on the application, many approaches are possible. In this paper we present a purely graph-theoretical approach, independent of the represented data. Based on the edge-connectivity of subgraphs, a tree of subgraphs is constructed, such that the children of a node are pairwise disjoint and contained in their parent. We describe a polynomial algorithm for the construction of the tree and present two heuristics, constructing the correct result in signi cantly decreased time. Furthermore we give a short description of possible applications in the elds of information retrieval, clustering and graph drawing. 1