Graph Wavelets for Multiscale Community Mining

We develop a signal processing approach to the multiscale detection of communities in networks, that is of groups of nodes well connected together. The method relies on carefully engineered wavelets on graphs to introduce the notion of scale and to obtain a local view of the graph from each node. Computing the correlations between wavelets centered at different nodes, one has access to a notion of similarity between nodes, thereby enabling a clustering procedure that groups nodes according to their community at the scale of analysis. By using a collection of random vectors to estimate the correlation between the nodes, we show that the method is suitable for the analysis of large graphs. Furthermore, we introduce a notion of partition stability and a statistical test allowing us to assess which scales of analysis of the network are relevant. The effectiveness of the method is discussed first on multiscale graph benchmarks, then on real data of social networks and on models for signal processing on graphs.