  We suggest a fast method to find possibly overlapping network communities of
a desired size and link density. Our method is a natural generalization of the
finite-$T$ superparamegnetic Potts clustering introduced by Blatt, Wiseman, and
Domany (Phys. Rev. Lett. v.76, 3251 (1996) and the recently suggested by
Reichard and Bornholdt (Phys. Rev. Lett. v.93, 21870 (2004)) annealing of Potts
model with global antiferromagnetic term. Similarly to both preceding works,
the proposed generalization is based on ordering of 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 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.
