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Assortativity and bidegree distributions on Bernoulli random graph superpositions
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- Journal:
- Probability in the Engineering and Informational Sciences / Volume 36 / Issue 4 / October 2022
- Published online by Cambridge University Press:
- 19 August 2021, pp. 1188-1213
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- Article
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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.
