Clique percolation in random networks |
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Authors: | Derényi Imre Palla Gergely Vicsek Tamás |
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Institution: | Department of Biological Physics, E?tv?s University, Pázmány P. stny. 1A, H-1117 Budapest, Hungary. |
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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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