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Preferential attachment graphs with co-existing types of different fitnesses

Part of: Stochastic processes Combinatorial probability Graph theory

Published online by Cambridge University Press:  16 January 2019

Jonathan Jordan
Jonathan Jordan*
Affiliation:
University of Sheffield
*
* Postal address: School of Mathematics and Statistics, University of Sheffield, Hounsfield Road, SheffieldS3 7RH, UK. Email address: jonathan.jordan@sheffield.ac.uk
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Abstract

We extend the work of Antunović et al. (2016) on competing types in preferential attachment models to include cases where the types have different fitnesses, which may be either multiplicative or additive. We show that, depending on the values of the parameters of the models, there are different possible limiting behaviours depending on the zeros of a certain function. In particular, we show the existence of choices of the parameters where one type is favoured both by having higher fitness and by the type of attachment mechanism, but the other type has a positive probability of dominating the network in the limit.

Keywords

Preferential attachmentcompeting typesfitness

MSC classification

Primary: 05C82: Small world graphs, complex networks
Secondary: 60C05: Combinatorial probability 60G99: None of the above, but in this section
Type
Research Papers
Information
Journal of Applied Probability , Volume 55 , Issue 4 , December 2018 , pp. 1211 - 1227
Copyright
Copyright © Applied Probability Trust 2018 

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