Percolation on correlated networks

TL;DR

This paper investigates how degree correlations in networks influence percolation thresholds and critical behavior, revealing conditions where correlations are irrelevant and identifying networks with unique percolation properties and critical exponents.

Contribution

It provides criteria for when degree correlations do not affect critical singularities and presents examples of networks with novel percolation behaviors due to assortative or disassortative mixing.

Findings

Degree correlations can be irrelevant for certain critical singularities.

Assortative and disassortative networks exhibit unusual percolation properties.

New critical exponents are identified in correlated networks.

Abstract

We reconsider the problem of percolation on an equilibrium random network with degree-degree correlations between nearest-neighboring vertices focusing on critical singularities at a percolation threshold. We obtain criteria for degree-degree correlations to be irrelevant for critical singularities. We present examples of networks in which assortative and disassortative mixing leads to unusual percolation properties and new critical exponents.