A continuous-time N-interaction random graph model

In this paper a continuous-time evolving random graph model is defined and examined. The main units of the model are complete graphs on N vertices, where N≥3 is a fixed integer. At each birth event a new vertex and random number of edges are added to the graph. The asymptotic behaviour of the number of vertices and the asymptotic behaviour of the number of m-cliques (2≤m≤N) are studied. The proofs are based on general results of the theory of branching processes.