Finding Strongly Knit Clusters in Social Networks

Social networks are ubiquitous. The discovery of close-knit clusters in these networks is of fundamental and practical interest. Existing clustering criteria are limited in that clusters typically do not overlap, all vertices are clustered and/or external sparsity is ignored. We introduce a new criterion that overcomes these limitations by combining internal density with external sparsity in a natural way. This paper explores combinatorial properties of internally dense and externally sparse clusters. A simple algorithm is given for provably finding such clusters assuming a sufficiently large gap between internal density and external sparsity. Experiments show that the algorithm is able to identify over 90% of the clusters in real graphs, assuming conditions on external sparsity.