Absence of epidemic threshold in scale-free networks with connectivity correlations

TL;DR

This paper demonstrates that in scale-free networks with diverging second moments, the epidemic threshold is absent regardless of connectivity correlations, impacting how infections spread in such networks.

Contribution

It provides an exact proof that diverging second moments in scale-free networks lead to no epidemic threshold, regardless of assortative or dissortative mixing.

Findings

No epidemic threshold in scale-free networks with diverging second moment.

Connectivity correlations do not prevent epidemic spreading in these networks.

Divergence of average nearest neighbors connectivity is key to this behavior.

Abstract

Random scale-free networks have the peculiar property of being prone to the spreading of infections. Here we provide an exact result showing that a scale-free connectivity distribution with diverging second moment is a sufficient condition to have null epidemic threshold in unstructured networks with either assortative or dissortative mixing. Connectivity correlations result therefore ininfluential for the epidemic spreading picture in these scale-free networks. The present result is related to the divergence of the average nearest neighbors connectivity, enforced by the connectivity detailed balance condition.