Preferential duplication graphs

Cohen, N., Jordan, J. and Voliotis, M. (2010) Preferential duplication graphs. Journal of Applied Probability , 47 (2). pp. 572-585. ISSN 0021-9002

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Abstract

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.

Item Type:	Article
Copyright, Publisher and Additional Information:	© 2010 Applied Probability Trust. This is an author produced version of a paper subsequently published in Journal of Applied Probability. Uploaded in accordance with the publisher's self-archiving policy.
Keywords:	Preferential duplication graphs; stochastic approximation; vertex-reinforced random walk
Academic Units:	The University of Sheffield > Faculty of Science (Sheffield) > School of Mathematics and Statistics (Sheffield)
Depositing User:	Miss Anthea Tucker
Date Deposited:	16 Aug 2010 08:41
Last Modified:	08 Feb 2013 17:01
Published Version:	http://dx.doi.org/10.1239/jap/1276784910
Status:	Published
Publisher:	Applied Probability Trust
Refereed:	Yes
Identification Number:	10.1239/jap/1276784910
URI:	http://eprints.whiterose.ac.uk/id/eprint/11115

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