Resilience to damage of graphs with degree correlations

TL;DR

This paper investigates how degree correlations in graphs affect their resilience to damage, providing general expressions for percolation thresholds and analyzing the impact of assortative and disassortative correlations.

Contribution

It introduces new analytical expressions for percolation thresholds in degree-correlated graphs and explores their influence on network resilience to damage.

Findings

Degree correlations significantly influence network robustness.

Provided bounds for percolation transition thresholds.

Assortative and disassortative correlations have contrasting effects on resilience.

Abstract

The existence or not of a percolation threshold on power law correlated graphs is a fundamental question for which a general criterion is lacking. In this work we investigate the problems of site and bond percolation on graphs with degree correlations and their connection with spreading phenomena. We obtain some general expressions that allow the computation of the transition thresholds or their bounds. Using these results we study the effects of assortative and disassortative correlations on the resilience to damage of networks.