Finding mesoscopic communities in sparse networks.

We suggest a fast method for finding possibly overlapping network communities of a desired size and link density. Our method is a natural generalization of the finite-T superparamagnetic Potts clustering introduced by Blatt et al (1996 Phys. Rev. Lett.76 3251) and the annealing of the Potts model with a global antiferromagnetic term recently suggested by Reichard and Bornholdt (2004 Phys. Rev. Lett.93 21870). Like in both cited works, the proposed generalization is based on ordering of the ferromagnetic Potts model; the novelty of the proposed approach lies in the adjustable dependence of the antiferromagnetic term on the population of each Potts state, which interpolates between the two previously considered cases. This adjustability allows one to empirically tune the algorithm to detect the maximum number of communities of the given size and link density. We illustrate the method by detecting protein complexes in high-throughput protein binding networks.