### Abstract

Motivated by the success of a k-clique percolation method for the identification of overlapping communities in large real networks, here we study the k-clique percolation problem in the Erdos-Rényi graph. When the probability p of two nodes being connected is above a certain threshold p _{c} (k), the complete subgraphs of size k (the k-cliques) are organized into a giant cluster. By making some assumptions that are expected to be valid below the threshold, we determine the average size of the k-clique percolation clusters, using a generating function formalism. From the divergence of this average size we then derive an analytic expression for the critical linking probability p _{c} (k).

Original language | English |
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Pages (from-to) | 219-227 |

Number of pages | 9 |

Journal | Journal of Statistical Physics |

Volume | 128 |

Issue number | 1-2 |

DOIs | |

Publication status | Published - Jul 1 2007 |

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### Keywords

- Community
- Network
- Percolation
- Random graph

### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics