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We analyze a dynamic random undirected graph in which newly added verticesare connected to those already present in the graph either using, withprobability $p$, an anti-preferential attachment mechanism or, with probability$1-p$, a preferential attachment mechanism. We derive the asymptotic degreedistribution in the general case and study the asymptotic behaviour of theexpected degree process in the general and that of the degree process in thepure anti-preferential attachment case. Degree homogenization mainly affectsconvergence rates for the former case and also the limiting degree distributionin the latter.

On dynamic random graphs with degree homogenization via anti-preferential attachment probabilities