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The N-star network evolution model

Part of: Graph theory Stochastic processes

Published online by Cambridge University Press:  30 July 2019

István Fazekas ,
Csaba Noszály  and
Attila Perecsényi
István Fazekas*
Affiliation:
University of Debrecen
Csaba Noszály*
Affiliation:
University of Debrecen
Attila Perecsényi*
Affiliation:
University of Debrecen
*
*Postal address: Faculty of Informatics, University of Debrecen, PO Box 400, 4002 Debrecen, Hungary.
*Postal address: Faculty of Informatics, University of Debrecen, PO Box 400, 4002 Debrecen, Hungary.
*Postal address: Faculty of Informatics, University of Debrecen, PO Box 400, 4002 Debrecen, Hungary.
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Abstract

A new network evolution model is introduced in this paper. The model is based on cooperations of N units. The units are the nodes of the network and the cooperations are indicated by directed links. At each evolution step N units cooperate, which formally means that they form a directed N-star subgraph. At each step either a new unit joins the network and it cooperates with N − 1 old units, or N old units cooperate. During the evolution both preferential attachment and uniform choice are applied. Asymptotic power law distributions are obtained both for in-degrees and for out-degrees.

Keywords

Random graphpreferential attachmentscale freepower lawsubmartingaleDoob–Meyer decomposition

MSC classification

Primary: 05C80: Random graphs 60G42: Martingales with discrete parameter
Type
Research Papers
Information
Journal of Applied Probability , Volume 56 , Issue 2 , June 2019 , pp. 416 - 440
Copyright
© Applied Probability Trust 2019 

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