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How Clustering Affects Epidemics in Random Networks

Part of: Mathematical sociology Graph theory Combinatorial probability

Published online by Cambridge University Press:  22 February 2016

Emilie Coupechoux  and
Marc Lelarge
Emilie Coupechoux*
Affiliation:
INRIA-ENS
Marc Lelarge*
Affiliation:
INRIA-ENS
*
∗ Current address: Laboratoire I3S, CS 40121, Université Nice Sophia Antipolis, 06903 Sophia Antipolis Cedex, France. Email address: [email protected]
∗∗ Postal address: INRIA-ENS, 23 avenue d'Italie, CS 81321, 75214 Paris Cedex 13, France.
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Abstract

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Motivated by the analysis of social networks, we study a model of random networks that has both a given degree distribution and a tunable clustering coefficient. We consider two types of growth process on these graphs that model the spread of new ideas, technologies, viruses, or worms: the diffusion model and the symmetric threshold model. For both models, we characterize conditions under which global cascades are possible and compute their size explicitly, as a function of the degree distribution and the clustering coefficient. Our results are applied to regular or power-law graphs with exponential cutoff and shed new light on the impact of clustering.

Keywords

Contagion thresholddiffusionrandom graphclustering

MSC classification

Primary: 60C05: Combinatorial probability
Secondary: 05C80: Random graphs 91D30: Social networks
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 46 , Issue 4 , December 2014 , pp. 985 - 1008
Copyright
© Applied Probability Trust 

Footnotes

This paper is part of the author's PhD thesis done at INRIA-ENS.

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