Asymptotics of m-Cliques in a Sparse Inhomogeneous Random Graph

Abstract

One of the classical questions in random graph theory is to understand the asymptotics of subgraph counts. In inhomogeneous random graph, this question has not been well studied. In this study, we investigate the asymptotic distribution of m-cliques in a sparse inhomogeneous random graph. Under mild conditions, we prove that the number of m-cliques converges in law to the standard normal distribution.