Multiscale community mining in networks using the graph wavelet transform of random vectors

In an effort to simplify the analysis of data represented by networks, a classical approach is to uncover the community structure of the underlying graph. In this work, we take advantage of graph wavelets and the associated natural definition of scale to propose a multi-scale community mining tool. More precisely, at a given scale, we cluster nodes in the same community when their corresponding wavelets are highly correlated. We show that the wavelet transform of a few random signals is sufficient to uncover correctly multi-scale communities in a graph. We test the method on a graph benchmark having hierarchical communities, before applying it to a real social network measured in a primary school.