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Preferential duplication graphs

Part of: Stochastic processes Graph theory Special processes

Published online by Cambridge University Press:  14 July 2016

Netta Cohen ,
Jonathan Jordan  and
Margaritis Voliotis
Netta Cohen*
Affiliation:
University of Leeds
Jonathan Jordan*
Affiliation:
University of Sheffield
Margaritis Voliotis*
Affiliation:
University of Leeds
*
∗Postal address: School of Computing, University of Leeds, Leeds, LS2 9JT, UK.
∗∗Postal address: Department of Probability and Statistics, University of Sheffield, Hicks Building, Sheffield, S3 7RH, UK. Email address: jonathan.jordan@shef.ac.uk
∗Postal address: School of Computing, University of Leeds, Leeds, LS2 9JT, UK.
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Abstract

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We consider a preferential duplication model for growing random graphs, extending previous models of duplication graphs by selecting the vertex to be duplicated with probability proportional to its degree. We show that a special case of this model can be analysed using the same stochastic approximation as for vertex-reinforced random walks, and show that ‘trapping’ behaviour can occur, such that the descendants of a particular group of initial vertices come to dominate the graph.

Keywords

Preferential duplication graphsstochastic approximationvertex-reinforced random walk

MSC classification

Secondary: 05C80: Random graphs 60G99: None of the above, but in this section 60K35: Interacting random processes; statistical mechanics type models; percolation theory
Type
Research Article
Information
Journal of Applied Probability , Volume 47 , Issue 2 , June 2010 , pp. 572 - 585
Copyright
Copyright © Applied Probability Trust 2010 

References

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