We present a rigorous and precise analysis of the maximum degree and the average degree in a dynamic duplication-divergence graph model introduced by Sol\'e, Pastor-Satorras et al. in which the graph grows according to a duplication-divergence mechanism, i.e. by iteratively creating a copy of some node and then randomly alternating the neighborhood of a new node with probability $p$. This model captures the growth of some real-world processes e.g. biological or social networks. In this paper, we prove that for some $0 < p < 1$ the maximum degree and the average degree of a duplication-divergence graph on $t$ vertices are asymptotically concentrated with high probability around $t^p$ and $\max\{t^{2 p - 1}, 1\}$, respectively, i.e. they are within at most a polylogarithmic factor from these values with probability at least $1 - t^{-A}$ for any constant $A > 0$.

翻译：我们针对Sole、Pastor-Satorras等人提出的动态复制-发散图模型中的最大度和平均度进行了严格而精确的分析。在该模型中，图通过复制-发散机制增长，即通过迭代地创建某个节点的副本，然后以概率$p$随机改变新节点的邻域。该模型捕捉了某些现实世界过程（例如生物或社交网络）的增长。在本文中，我们证明对于某些$0 < p < 1$，包含$t$个顶点的复制-发散图的最大度和平均度分别高概率渐近集中在$t^p$和$\max\{t^{2 p - 1}, 1\}$附近，即对于任意常数$A > 0$，它们与这些值的差距最多为多对数因子，且概率至少为$1 - t^{-A}$。