论文标题
Bernoulli随机图叠加上的分类性和双层分布
Assortativity and bidegree distributions on Bernoulli random graph superpositions
论文作者
论文摘要
具有$ n $节点和$ m $重叠层的概率生成网络模型，作为$ M $独立的Bernoulli随机图的叠加，具有变化的大小和强度。当$ n $和$ m $很大并且具有相同数量级的顺序时，该模型承认具有可调的幂律学位分布和非呈现聚类系数的稀疏限制性制度。在本文中，我们证明了一个用于相邻节点联合度分布的渐近公式。这为模型分类性提供了一个简单的分析公式，并打开了分析秩相关系数的方法，适用于具有重尾分布的随机图。我们还研究了电力法对渐近联合程度分布的影响。
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.
