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# A continuous-time *N*-interaction random graph model

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posted on 2023-11-21, 07:40 authored by Bettina PorvázsnyikIn 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.