External-Memory network analysis algorithms for naturally sparse graphs

Abstract

In this paper, we present a number of network-analysis algorithms in the external-memory model. We focus on methods for large naturally sparse graphs, that is, n-vertex graphs that have O(n) edges and are structured so that this sparsity property holds for any subgraph of such a graph. We give efficient external-memory algorithms for the following problems for such graphs: 1 Finding an approximate d-degeneracy ordering. 2 Finding a cycle of length exactly c. 3 Enumerating all maximal cliques. Such problems are of interest, for example, in the analysis of social networks, where they are used to study network cohesion. © 2011 Springer-Verlag Berlin Heidelberg.