Percolation of random clique networks

We propose a random clique network (RCN), which is constructed by adding cliques randomly. In a k-clique, there are k nodes which are connected each other completely. The RCN possesses some characters of the small world network and the modular hierarchical structure. At k=2, the RCN becomes the Erdös-Rényi (ER) random network. In of the largest cluster inDthis paper, we study the percolation transition of RCN by investigating the biggest size gap the network and the corresponding evolution step, which is taken as the transition point. From the Monte Carlo Dsimulations of RCN at k=2, 3, 4, 5, we can calculate the mean values and the mean square root of fluctuations for and the transition point. They all show a power-law dependence on the network size N. This leads to the conclusion that the percolation transitions of RCN at k=2, 3, 4, 5 are continuous. From the exponents of power-law behaviors, the critical exponents β₁, v₁ of Δ and the critical exponents β₂, v₂ of the transition points can be obtained. These critical exponents of different RCN are shown to be independent of the clique size k. The percolation transitions of RCN belong to the same universality class as the ER random network.