  Detecting community structure in real-world networks is a challenging
problem. Recently, it has been shown that the resolution of methods based on
optimizing a modularity measure or a corresponding energy is limited;
communities with sizes below some threshold remain unresolved. One possibility
to go around this problem is to vary the threshold by using a tuning parameter,
and investigate the community structure at variable resolutions. Here, we
analyze the resolution limit and multiresolution behavior for two different
methods: a q-state Potts method proposed by Reichard and Bornholdt, and a
recent multiresolution method by Arenas, Fernandez, and Gomez. These methods
are studied analytically, and applied to three test networks using simulated
annealing.
