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Degree sequences of geometric preferential attachment graphs

Part of: Geometric probability and stochastic geometry Graph theory

Published online by Cambridge University Press:  01 July 2016

Jonathan Jordan
Jonathan Jordan*
Affiliation:
University of Sheffield
*
∗ Postal address: Department of Probability and Statistics, University of Sheffield, Hicks Building, Sheffield S3 7RH, UK. Email address: jonathan.jordan@shef.ac.uk
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Abstract

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We investigate the degree sequence of the geometric preferential attachment model of Flaxman, Frieze and Vera (2006), (2007) in the case where the self-loop parameter α is set to 0. We show that, given certain conditions on the attractiveness function F, the degree sequence converges to the same sequence as found for standard preferential attachment in Bollobás et al. (2001). We also apply our method to the extended model introduced in van der Esker (2008) which allows for an initial attractiveness term, proving similar results.

Keywords

Geometric random graphpreferential attachment

MSC classification

Primary: 05C80: Random graphs
Secondary: 60D05: Geometric probability and stochastic geometry
Type
Stochastic Geometry and Statistical Applications
Information
Advances in Applied Probability , Volume 42 , Issue 2 , June 2010 , pp. 319 - 330
Copyright
Copyright © Applied Probability Trust 2010 

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