Clique percolation in random networks

Imre Derenyi; Gergely Palla; Tamas Vicsek

doi:10.1103/physrevlett.94.160202

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Clique percolation in random networks

Imre Derenyi·Gergely Palla·Tamas 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-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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Imre Derenyi, Gergely Palla, Tamas Vicsek. 2005-04-21. Clique percolation in random networks. https://doi.org/10.1103/physrevlett.94.160202

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