Limited resolution and multiresolution methods in complex network community detection

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 function 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 Reichardt and Bornholdt,
and a recent multiresolution method by Arenas, Fern´andez, and G´omez. These methods
are studied analytically, and applied to three test networks using simulated annealing.

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