We analyze a dynamic random undirected graph in which newly added vertices are connected to those already present in the graph either using, with probability $p$, an anti-preferential attachment mechanism or, with probability $1-p$, a preferential attachment mechanism. We derive the asymptotic degree distribution in the general case and study the asymptotic behavior of the expected degree process in the general and that of the degree process in the pure anti-preferential attachment case. Degree homogenization mainly affects convergence rates for the former case and also the limiting degree distribution in the latter. Lastly, we perform a simulative study of a variation of the introduced model allowing for anti-preferential attachment probabilities given in terms of the current maximum degree of the graph.

我们分析了一个动态随机无向图，其中使用概率将新添加的顶点连接到图中已经存在的顶点 $p$，反优惠依恋机制或 $\mathrm{1个}-p$，一种优先的依恋机制。我们推导了一般情况下的渐近度分布，并研究了一般情况下期望度过程和纯反优惠依恋情况下的度过程的渐近行为。度均化主要影响前者的收敛速度，也影响后者的极限度分布。最后，我们对引入模型的变体进行了模拟研究，该模型允许根据图形的当前最大程度给出反优先附着概率。