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Asymptotic Properties of a Random Graph with Duplications

Part of: Stochastic processes Graph theory

Published online by Cambridge University Press:  30 January 2018

Ágnes Backhausz  and
Tamás F. Móri
Ágnes Backhausz*
Affiliation:
Eötvös Loránd University
Tamás F. Móri*
Affiliation:
Eötvös Loránd University
*
∗ Postal address: MTA Alfréd Rényi Institute of Mathematics, Pázmány P. s. 1/C, H-1117, Budapest, Hungary. Email address: agnes@math.elte.hu
∗∗ Postal address: Department of Probability Theory and Statistics, Pázmány P. s. 1/C, H-1117, Budapest, Hungary. Email address: mori@math.elte.hu
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Abstract

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We deal with a random graph model evolving in discrete time steps by duplicating and deleting the edges of randomly chosen vertices. We prove the existence of an almost surely asymptotic degree distribution, with stretched exponential decay; more precisely, the proportion of vertices of degree d tends to some positive number cd > 0 almost surely as the number of steps goes to ∞, and cd ~ (eπ)1/2d1/4e-2√d holds as d → ∞.

Keywords

Scale-freeduplicationdeletionrandom graphmartingale

MSC classification

Primary: 60G42: Martingales with discrete parameter
Secondary: 05C80: Random graphs
Type
Research Article
Information
Journal of Applied Probability , Volume 52 , Issue 2 , June 2015 , pp. 375 - 390
Copyright
© Applied Probability Trust 

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