General clique percolation in random networks

Jingfang Fan, Xiaosong Chen

Research output: Contribution to journalArticlepeer-review

16 Scopus citations


A general (k, l) clique community of a network, which consists of adjacent k-cliques sharing at least l vertices with k - 1 = l = 1, is introduced. With the emergence of a giant (k, l) clique community in the network, there is a (k, l) clique percolation. Using the largest size jump . of the largest clique community during network evolution and the corresponding evolution step Tc, we study the general (k, l) clique percolation of the Erd.os-Rényi network. We investigate the averages of . and Tc and their fluctuations for different network size N. The clique percolation can be identified by the power-law finite-size effects of the averages and root mean squares of fluctuation. The finite-size scaling distribution functions of fluctuations are calculated. The universality class of the (k, l) clique percolation is characterized by the critical exponents of power-law finite-size effects. Using Monte Carlo simulations, we find that the Erd.os-Rényi network experiences a series of (k, l) clique percolation with (k, l) = (2, 1), (3, 1), (3, 2), (4, 1), (4, 2), (4, 3), (5, 1). We find that the critical exponents and therefore the universality class of the (k, l) clique percolation depend on clique connection index l, but are independent of clique size k.

Original languageEnglish
Article number28005
Issue number2
StatePublished - 1 Jul 2014
Externally publishedYes

ASJC Scopus subject areas

  • General Physics and Astronomy


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