### 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.

Original language | English |
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Article number | 160202 |

Journal | Physical review letters |

Volume | 94 |

Issue number | 16 |

DOIs | |

Publication status | Published - Apr 29 2005 |

### ASJC Scopus subject areas

- Physics and Astronomy(all)

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## Cite this

*Physical review letters*,

*94*(16), [160202]. https://doi.org/10.1103/PhysRevLett.94.160202