Epidemic thresholds on scale-free graphs: the interplay between exponent and preferential choice

TL;DR

This paper investigates how the epidemic threshold in scale-free networks depends on the degree distribution exponent and the connectivity among high-degree nodes, revealing that clustering impacts epidemic spread.

Contribution

It demonstrates that degree distribution alone is insufficient to determine epidemic thresholds; the connectivity among high-degree nodes is crucial.

Findings

Epidemic thresholds are influenced by the connectivity among high-degree vertices.

Absence of epidemic threshold correlates with a large cluster of bounded diameter.

Degree distribution exponent less than three does not alone determine epidemic threshold properties.

Abstract

We show for a model of scale-free graphs with biased partner choice that knowing the exponent for the degree distribution is in general not sufficient to decide epidemic threshold properties for exponents less than three.We show that the connectivity between the high degree vertices and therefore the diameter is the relevant geometric quantity for epidemic threshold estimations.Absence of epidemic threshold happens precisely when a positive fraction of the nodes form a cluster of bounded diameter.