Cascades on correlated and modular random networks

An analytical approach to determining the mean avalanche size in a broad class of dynamical models on random networks is introduced. Previous results on percolation transitions and epidemic sizes are shown to be special cases of the method. The time-dependence of cascades and extensions to networks...

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Bibliographic Details
Published in:Physical review. E, Statistical, nonlinear, and soft matter physics Statistical, nonlinear, and soft matter physics, 2008-04, Vol.77 (4 Pt 2), p.046117-046117
Main Author: Gleeson, James P
Format: Article
Language:English
Online Access:Get full text
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Summary:An analytical approach to determining the mean avalanche size in a broad class of dynamical models on random networks is introduced. Previous results on percolation transitions and epidemic sizes are shown to be special cases of the method. The time-dependence of cascades and extensions to networks with community structure or degree-degree correlations are discussed. Analytical results for the rate of spread of innovations in a modular network and for the size of k cores in networks with degree-degree correlations are confirmed with numerical simulations.
ISSN:1539-3755
DOI:10.1103/PhysRevE.77.046117