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Chin. Phys. B, 2016, Vol. 25(6): 060202    DOI: 10.1088/1674-1056/25/6/060202
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Degree distribution of random birth-and-death network with network size decline

Xiao-Jun Zhang(张晓军), Hui-Lan Yang(杨会兰)
School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu 611731, China
Abstract  

In this paper, we provide a general method to obtain the exact solutions of the degree distributions for random birth-and-death network (RBDN) with network size decline. First, by stochastic process rules, the steady state transformation equations and steady state degree distribution equations are given in the case of m ≥ 3 and 0< p< 1/2, then the average degree of network with n nodes is introduced to calculate the degree distributions. Specifically, taking m=3 for example, we explain the detailed solving process, in which computer simulation is used to verify our degree distribution solutions. In addition, the tail characteristics of the degree distribution are discussed. Our findings suggest that the degree distributions will exhibit Poisson tail property for the declining RBDN.

Keywords:  random birth-and-death network (RBDN)      Markov chain      generating function      degree distribution  
Received:  04 January 2016      Revised:  04 February 2016      Accepted manuscript online: 
PACS:  02.50.Ga (Markov processes)  
  02.60.Cb (Numerical simulation; solution of equations)  
  64.60.aq (Networks)  
Fund: 

Project supported by the National Natural Science Foundation of China (Grant No. 61273015) and the Chinese Scholarship Council.

Corresponding Authors:  Xiao-Jun Zhang     E-mail:  sczhxj@uestc.edu.cn

Cite this article: 

Xiao-Jun Zhang(张晓军), Hui-Lan Yang(杨会兰) Degree distribution of random birth-and-death network with network size decline 2016 Chin. Phys. B 25 060202

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