Robustness and Assortativity for Diffusion-like Processes in Scale-free Networks

TL;DR

This paper investigates how network assortativity affects the spread of epidemics and failures in scale-free networks, revealing that disassortative networks are more robust and easier to immunize, while assortative networks are more vulnerable but can be protected with targeted strategies.

Contribution

It provides a spectral analysis of diffusion thresholds and times in relation to network assortativity, and demonstrates the impact of immunization policies on network resilience.

Findings

Disassortative networks have higher epidemic thresholds.

Assortative networks exhibit longer diffusion times.

Degree-targeted immunization enhances resilience in assortative networks.

Abstract

By analysing the diffusive dynamics of epidemics and of distress in complex networks, we study the effect of the assortativity on the robustness of the networks. We first determine by spectral analysis the thresholds above which epidemics/failures can spread; we then calculate the slowest diffusional times. Our results shows that disassortative networks exhibit a higher epidemiological threshold and are therefore easier to immunize, while in assortative networks there is a longer time for intervention before epidemic/failure spreads. Moreover, we study by computer simulations the sandpile cascade model, a diffusive model of distress propagation (financial contagion). We show that, while assortative networks are more prone to the propagation of epidemic/failures, degree-targeted immunization policies increases their resilience to systemic risk.