Clique percolation in random networks
Disordered Systems and Neural Networks
2007-05-23 v1 Statistical Mechanics
Biological Physics
Abstract
The notion of k-clique percolation in random graphs is introduced, where k is the size of the complete subgraphs whose large scale organizations are analytically and numerically investigated. For the Erdos-Renyi graph of N vertices we obtain that the percolation transition of k-cliques takes place when the probability of two vertices being connected by an edge reaches the threshold pc(k)=[(k-1)N]^{-1/(k-1)}. At the transition point the scaling of the giant component with N is highly non-trivial and depends on k. We discuss why clique percolation is a novel and efficient approach to the identification of overlapping communities in large real networks.
Cite
@article{arxiv.cond-mat/0504551,
title = {Clique percolation in random networks},
author = {Imre Derenyi and Gergely Palla and Tamas Vicsek},
journal= {arXiv preprint arXiv:cond-mat/0504551},
year = {2007}
}
Comments
4 pages, 3 figures, to be published in Phys. Rev. Lett