Assortativity and bidegree distributions on Bernoulli random graph superpositions
- Full version (32 pages)
- Probability in the Engineering and Informational Sciences 36(4):1188–1213, 2022
- Published online: 19 Aug 2021
- doi:10.1017/S0269964821000310
- arXiv:2002.11809
- Short version (14 pages)
- 17th Workshop on Algorithms and Models for the Web Graph (WAW), 2020
- Lecture Notes in Computer Science 12091, pp. 68–81, Springer 2020
- doi:10.1007/978-3-030-48478-1_5
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. This article presents 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.