analyzing the cliquesin scale-free random graphs

In this paper, we study the size of the largest clique, namely the cliquenumber, in a random graph model g(n, τ) on n vertices, which has degree distributionwith regularly varying tail with scaling exponent τ −1. we prove stochastic convergenceproperties for clique number ω(g(n, τ)) as n goes to infinity. our results show that thereis a major difference in the clique number ω(g(n, τ)) between the case τ < 3 and τ > 3with an intermediate result for τ = 3.