  We focus on the detection of communities in multi-scale networks, namely
networks made of different levels of organization and in which modules exist at
different scales. It is first shown that methods based on modularity are not
appropriate to uncover modules in empirical networks, mainly because modularity
optimization has an intrinsic bias towards partitions having a characteristic
number of modules which might not be compatible with the modular organization
of the system. We argue for the use of more flexible quality functions
incorporating a resolution parameter that allows us to reveal the natural
scales of the system. Different types of multi-resolution quality functions are
described and unified by looking at the partitioning problem from a dynamical
viewpoint. Finally, significant values of the resolution parameter are selected
by using complementary measures of robustness of the uncovered partitions. The
methods are illustrated on a benchmark and an empirical network.
