Chapter

Percolation and epidemics

Sergey N. Dorogovtsev

in Lectures on Complex Networks

Published in print February 2010 | ISBN: 9780199548927
Published online May 2010 | e-ISBN: 9780191720574 | DOI: http://dx.doi.org/10.1093/acprof:oso/9780199548927.003.0006

Series: Oxford Master Series in Physics

Percolation and epidemics

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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

Chapter.  5512 words.  Illustrated.

Subjects: Mathematical and Statistical Physics

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