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Title of Journal: J Stat Phys

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Abbravation: Journal of Statistical Physics

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Springer US

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DOI

10.1007/s00259-015-3115-5

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1572-9613

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Random BirthandDeath Networks

Authors: Xiaojun Zhang Zheng He Lez RaymanBacchus
Publish Date: 2016/01/13
Volume: 162, Issue: 4, Pages: 842-854
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Abstract

In this paper a baseline model termed as random birthanddeath network RBDN model is considered in which at each time step a new node is added into the network with probability p 0p1 and connected to m old nodes uniformly or an existing node is deleted from the network with probability q=1p This model allows for fluctuations in size reflecting the behaviour of networks in many different disciplines including physics ecology and economics The purpose of this study is to develop the RBDN model and explore its basic statistical properties For different p we first discuss the network size of RBDN then combining the stochastic process rules based Markov chain method and the probability generating function method we provide the exact solutions of the degree distributions Finally the tail characteristics of the degree distributions are explored after simulation verification Our results show that the tail of the degree distribution for RBDN exhibits a Poisson tail in the case of 0ple 1/2 and an exponential tail as p approaches to 1

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