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 $N\ge 3$ 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 ($2\le m\le N$) are studied. The proofs are based on general results of the theory of branching processes.