ANALYZING THE CLIQUES IN SCALE-FREE RANDOM GRAPHS

In this paper, we study the size of the largest clique, namely the clique number, in a random graph model G(n, τ) on n vertices, which has degree distribution with regularly varying tail with scaling exponent τ −1. We prove stochastic convergence properties for clique number ω(G(n, τ)) as n goes to infinity. Our results show that there is a major difference in the clique number ω(G(n, τ)) between the case τ 3 and τ 3 with an intermediate result for τ = 3.