Network topology near criticality in adaptive epidemics

TL;DR

This paper investigates how structural network measures change near the critical point of epidemic spread in adaptive networks, identifying potential early-warning indicators for network collapse.

Contribution

It clarifies which network measures can serve as early-warning signs of phase transition in adaptive epidemic networks, focusing on topology and dynamics interplay.

Findings

$SI$ link density and triplet densities peak near criticality

Certain measures like degree and harmonic mean distance do not signal the transition

Multiple network measures exhibit maxima or minima close to the critical infection rate

Abstract

We study structural changes of adaptive networks in the co-evolutionary susceptible-infected-susceptible (SIS) network model along its phase transition. We clarify to what extent these changes can be used as early-warning signs for the transition at the critical infection rate $\lambda_c$ at which the network collapses and the system disintegrates. We analyze the interplay between topology and node-state dynamics near criticality. Several network measures exhibit clear maxima or minima close to the critical threshold that could potentially serve as early-warning signs. These measures include the $SI$ link density, triplet densities, clustering, assortativity and the eigenvalue gap. For the $SI$ link density and triplet densities the maximum is found to originate from the co-existence of two power laws. Other network quantities, such as the degree, the branching ratio, or the harmonic mean distance, show scaling with a singularity at $\lambda=0$ and not at $\lambda_c$, which means that they are incapable of detecting the transition.