A probabilistic generative network model with $n$ nodes and $m$ overlapping layers is obtained as a superposition of $m$ mutually independent Bernoulli random graphs of varying size and strength. When $n$ and $m$ are large and of the same order of magnitude, the model admits a sparse limiting regime with a tunable power-law degree distribution and nonvanishing clustering coefficient. In this article, we prove an asymptotic formula for the joint degree distribution of adjacent nodes. This yields a simple analytical formula for the model assortativity and opens up ways to analyze rank correlation coefficients suitable for random graphs with heavy-tailed degree distributions. We also study the effects of power laws on the asymptotic joint degree distributions.

具有$n$个节点和$m$个重叠层的概率生成网络模型是作为$m$个不同大小和强度的相互独立的伯努利随机图的叠加而获得的。当$n$和$m$大且数量级相同，该模型承认具有可调节幂律度分布和非零聚类系数的稀疏限制机制。在本文中，我们证明了相邻节点的联合度分布的渐近公式。这产生了模型分类性的简单分析公式，并开辟了分析适用于具有重尾度分布的随机图的等级相关系数的方法。我们还研究了幂律对渐近联合度分布的影响。