### 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 |

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### ASJC Scopus subject areas

- Physics and Astronomy(all)
- Medicine(all)

### Cite this

*Physical Review Letters*,

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

**Clique percolation in random networks.** / Derényi, I.; Palla, Gergely; Vicsek, T.

Research output: Contribution to journal › Article

*Physical Review Letters*, vol. 94, no. 16, 160202. https://doi.org/10.1103/PhysRevLett.94.160202

}

TY - JOUR

T1 - Clique percolation in random networks

AU - Derényi, I.

AU - Palla, Gergely

AU - Vicsek, T.

PY - 2005/4/29

Y1 - 2005/4/29

N2 - 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 pc(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.

AB - 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 pc(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.

UR - http://www.scopus.com/inward/record.url?scp=18144393488&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=18144393488&partnerID=8YFLogxK

U2 - 10.1103/PhysRevLett.94.160202

DO - 10.1103/PhysRevLett.94.160202

M3 - Article

C2 - 15904198

AN - SCOPUS:18144393488

VL - 94

JO - Physical Review Letters

JF - Physical Review Letters

SN - 0031-9007

IS - 16

M1 - 160202

ER -