2020/02/26 by Mindaugas Bloznelis, Bloznelis, Mindaugas, Joona Karjalainen +3
Mathematics · Physics and Astronomy · #60B10 #60C05 #62G35 #91D30 #Complex Network Analysis Techniques #FOS: Computer and information sciences #FOS: Mathematics #G.2.2 #G.3 #J.4 #Opinion Dynamics and Social Influence #Probability (math.PR) #Social and Information Networks (cs.SI) #Statistics Theory (math.ST) #Stochastic processes and statistical mechanics
paper · pdf · doi:10.48550/arxiv.2002.11809
openalex publication_date 2020/02/26 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28
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.