Clique percolation in random graphs.

As a generation of the classical percolation, clique percolation focuses on the connection of cliques in a graph, where the connection of two k cliques means that they share at least l1 makes a step-function-like discontinuous phase transition in the thermodynamic limit and a continuous phase transition for l=1. More interesting, our analysis shows that at the critical point, the order parameter ϕ(c) for l>1 is neither 0 nor 1, but a constant depending on k and l. All these theoretical findings are in agreement with the simulation results, which give theoretical support and clarification for previous simulation studies of clique percolation.