Weights of Cliques in a Random Graph Model Based on Three-Interactions

Abstract

A random graph evolution rule is considered. The graph evolution is based on interactions of three vertices. The weight of a clique is the number of its interactions. The asymptotic behaviour of the weights is described. It is known that the weight distribution of the vertices is asymptotically a power law. Here it is proved that the weight distributions both of the edges and the triangles are also asymptotically power laws. The proofs are based on discrete time martingale methods. Some numerical results are also presented.