General Clique Percolation in Network Evolution [article]

Jingfang Fan, Xiaosong Chen
2013 arXiv   pre-print
We introduce a general (k,l) clique community, which consists of adjacent k-cliques sharing at least l vertices with k-1 > l > 1. The emergence of a giant (k,l) clique community indicates a (k,l) clique percolation, which is studied by the largest size gap Δ of the largest clique community during network evolution and the corresponding evolution step T_c. For a clique percolation, the averages of Δ and T_c and the root-mean-squares of their fluctuations have power law finite-size effects whose
more » ... xponents are related to the critical exponents. The fluctuation distribution functions of Δ and T_c follow a finite-size scaling form. In the evolution of the Erdős-Rényi network, there are a series of (k,l) clique percolation with (k,l)=(2,1),(3,1),(3,2),(4,1),(4,2),(5,1),(4,3), and so on. The critical exponents of clique percolation depend on l, but are independent of k. The universality class of a (k,l) clique percolation is characterized alone by l.
arXiv:1309.4535v1 fatcat:bgpqwjxjtjexvdpse56ekznt6a