  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.
