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Lectures on Complex Networks$
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Sergey Dorogovtsev

Print publication date: 2010

Print ISBN-13: 9780199548927

Published to Oxford Scholarship Online: May 2010

DOI: 10.1093/acprof:oso/9780199548927.001.0001

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Percolation and epidemics

Percolation and epidemics

Chapter:
(p.41) 6 Percolation and epidemics
Source:
Lectures on Complex Networks
Author(s):

Sergey N. Dorogovtsev

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780199548927.003.0006

This chapter considers the organization of connected components in uncorrelated networks, in particular, the structure and size of a giant connected component. These properties are closely related to the percolation properties of these networks. The value of the percolation threshold for various degree distributions is estimated, and the resilience of scale-free networks against random failures is described. The hierarchical organization of k-cores in these networks is discussed. A few basic epidemic models on complex networks are introduced, and the evolution of diseases in networks is described.

Keywords:   connected components, percolation, percolation threshold, ultra-resilience phenomenon, k-cores, epidemic threshold

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