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

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

2002-08-08

arxiv.org/abs/cond-mat/0208163v1

Physics

Condensed Matter

Statistical Mechanics

Scientific paper

10.1103/PhysRevLett.90.028701

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.

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