arXiv:cond-mat/0208163cond-mat.stat-mech
Absence of epidemic threshold in scale-free networks with connectivity correlations
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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.
Real networks are not lattices; they have varied degree distributions. The famous result of Marián Boguña and Alessandro Vespignani shows, that for scale-free networks (which closely resemble the networks we see in the real world), the epidemic threshold could be arbitrarily…
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