Assortativity and bidegree distributions on Bernoulli random graph superpositions

Mindaugas Bloznelis, Joona Karjalainen, Lasse Leskelä
2021 Probability in the engineering and informational sciences (Print)  
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
more » ... 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.
doi:10.1017/s0269964821000310 fatcat:zum4bgvzyjbdnlxkexhfoubmpe