Finding mesoscopic communities in sparse networks

Abstract

We suggest a fast method for finding possibly overlapping network communities ofa desired size and link density. Our method is a natural generalization of thefinite-T superparamagnetic Potts clustering introduced by Blatt et al (1996 Phys. Rev. Lett. 763251) and the annealing of the Potts model with a global antiferromagnetic termrecently suggested by Reichardt and Bornholdt (2004 Phys. Rev. Lett. 93 218701).Like in both cited works, the proposed generalization is based on ordering ofthe ferromagnetic Potts model; the novelty of the proposed approach lies in theadjustable dependence of the antiferromagnetic term on the population of eachPotts state, which interpolates between the two previously considered cases. Thisadjustability allows one to empirically tune the algorithm to detect the maximumnumber of communities of the given size and link density. We illustrate the methodby detecting protein complexes in high-throughput protein binding networks.