A Game-Theoretic Approach to Graph Clustering

Abstract

The last decade has witnessed an explosion in the modeling of complex systems. Predominantly, graphs are used to represent these systems. The problem of detecting overlapping clusters in graphs is of utmost importance. We present a novel definition of overlapping clusters. A noncooperative game is proposed such that the equilibrium conditions of the game correspond to the clusters in the graph. Several properties of the game are analyzed and exploited to show the existence of a pure Nash equilibrium (NE) and compute it effectively. We present two algorithms to compute NE and prove their convergence. Empirically, the running times of both algorithms are nearly linear in the number of edges. Also, one of the algorithms can be readily parallelized, making it scalable. Finally, our approach is compared with existing overlapping cluster detection algorithms and validated on several artificial and real data sets.