Multiscale Community Mining in Networks Using Spectral Graph Wavelets

For data represented by networks, the community structure of the underlying graph is of great interest. A classical clustering problem is to uncover the overall ``best'' partition of nodes in communities. Here, a more elaborate description is proposed in which community structures are identified at different scales. To this end, we take advantage of the local and scale-dependent information encoded in graph wavelets. After new developments for the practical use of graph wavelets, studying proper scale boundaries and parameters and introducing scaling functions, we propose a method to mine for communities in complex networks in a scale-dependent manner. It relies on classifying nodes according to their wavelets or scaling functions, using a scale-dependent modularity function. An example on a graph benchmark having hierarchical communities shows that we estimate successfully its multiscale structure.