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Clique percolation in random networks.

Imre Derényi·Gergely Palla·Tamás Vicsek
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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-Rényi 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 p(c) (k) = [(k - 1)N](-1/(k - 1)). At the transition point the scaling of the giant component with N is highly nontrivial 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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Imre Derényi, Gergely Palla, Tamás Vicsek. 2005-04-29. Clique percolation in random networks.. https://doi.org/10.1103/physrevlett.94.160202

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