Open Access
January 2013 Random networks with sublinear preferential attachment: The giant component
Steffen Dereich, Peter Mörters
Ann. Probab. 41(1): 329-384 (January 2013). DOI: 10.1214/11-AOP697


We study a dynamical random network model in which at every construction step a new vertex is introduced and attached to every existing vertex independently with a probability proportional to a concave function $f$ of its current degree. We give a criterion for the existence of a giant component, which is both necessary and sufficient, and which becomes explicit when $f$ is linear. Otherwise it allows the derivation of explicit necessary and sufficient conditions, which are often fairly close. We give an explicit criterion to decide whether the giant component is robust under random removal of edges. We also determine asymptotically the size of the giant component and the empirical distribution of component sizes in terms of the survival probability and size distribution of a multitype branching random walk associated with $f$.


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Steffen Dereich. Peter Mörters. "Random networks with sublinear preferential attachment: The giant component." Ann. Probab. 41 (1) 329 - 384, January 2013.


Published: January 2013
First available in Project Euclid: 23 January 2013

zbMATH: 1260.05143
MathSciNet: MR3059201
Digital Object Identifier: 10.1214/11-AOP697

Primary: 05C80
Secondary: 60C05 , 90B15

Keywords: Barabási–Albert model , cluster , dynamic random graph , Erdős–Rényi model , Giant component , multitype branching random walk , nonlinear preferential attachment , power law , Scale-free network

Rights: Copyright © 2013 Institute of Mathematical Statistics

Vol.41 • No. 1 • January 2013
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