Clique percolation in random networks

Details Clique percolation in random networks Clique percolation in random networks

2005-04-21

arxiv.org/abs/cond-mat/0504551v1

Phys. Rev. Lett. 94, 160202 (2005)

Physics

Condensed Matter

Disordered Systems and Neural Networks

4 pages, 3 figures, to be published in Phys. Rev. Lett

Scientific paper

10.1103/PhysRevLett.94.160202

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.

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