Random degree-degree correlated networks

TL;DR

This paper investigates how degree-degree correlations influence key structural properties of networks, using ensembles constrained by a fixed correlation measure, and examines their effects on spreading processes.

Contribution

It introduces a method to generate network ensembles with specified degree correlations and analyzes their structural properties and bounds.

Findings

Degree correlations affect transitivity, branching, and characteristic lengths.

Correlation bounds depend on network size and degree distribution.

Networks with different degree distributions respond differently to correlation tuning.

Abstract

Correlations may affect propagation processes on complex networks. To analyze their effect, it is useful to build ensembles of networks constrained to have a given value of a structural measure, such as the degree-degree correlation $r$, being random in other aspects and preserving the degree distribution. This can be done through Monte Carlo optimization procedures. Meanwhile, when tuning $r$, other network properties may concomitantly change. Then, in this work we analyze, for the $r$-ensembles, the impact of $r$ on properties such as transitivity, branching and characteristic lengths, that are relevant when investigating spreading phenomena on these networks. The present analysis is performed for networks with degree distributions of two main types: either localized around a typical degree (with exponentially bounded asymptotic decay) or broadly distributed (with power-law decay). Correlation bounds and size effects are also investigated.