Assortativity and bidegree distributions on Bernoulli random graph superpositions

Mindaugas Bloznelis, Joona Karjalainen, Lasse Leskelä

Research output: Contribution to journalArticleScientificpeer-review

Abstract

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.
Original languageEnglish
Number of pages26
JournalProbability in the Engineering and Informational Sciences
DOIs
Publication statusPublished - 19 Aug 2021
MoE publication typeA1 Journal article-refereed

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