Graph clustering based on mixing time of random walks

Clustering of a graph is the task of grouping its nodes in such a way that the nodes within the same cluster are well connected, but they are less connected to nodes in different clusters. In this paper we propose a clustering metric based on the random walks´ properties to evaluate the quality of a graph clustering. We also propose a randomized algorithm that identifies a locally optimal clustering of the graph according to the metric defined. The algorithm is intrinsically distributed and asynchronous. If the graph represents an actual network where nodes have computing capabilities, each node can determine its own cluster relying only on local communications. We show that the size of clusters can be adapted to the available processing capabilities to reduce the algorithm´s complexity.