Networks with degree-degree correlations is a special case of edge-coloured random graphs

TL;DR

This paper models networks with degree-degree correlations as edge-coloured random graphs, revealing unique percolation behaviors and implications for network robustness and spreading phenomena.

Contribution

It introduces a framework linking degree correlations to edge-coloured graphs, enabling analysis of percolation and robustness in correlated networks.

Findings

Degree correlations can cause unexpected sensitivity in component sizes.

Networks may have a vanishing percolation threshold despite finite degree moments.

Correlated networks can facilitate super spreading without prominent hubs.

Abstract

In complex networks the degrees of adjacent nodes may often appear dependent -- which presents a modelling challenge. We present a working framework for studying networks with an arbitrary joint distribution for the degrees of adjacent nodes by showing that such networks are a special case of edge-coloured random graphs. We use this mapping to study bond percolation in networks with assortative mixing and show that, unlike in networks with independent degrees, the sizes of connected components may feature unexpected sensitivity to perturbations in the degree distribution. The results also indicate that degree-degree dependencies may feature a vanishing percolation threshold even when the second moment of the degree distribution is finite. These results may be used to design artificial networks that efficiently withstand link failures and indicate possibility of super spreading in networks without clearly distinct hubs