Degree distribution of random birth-and-death network with network size decline

doi:10.1088/1674-1056/25/6/060202

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

[1]	Barábasi A L and Albert R 1999 Science 286 5439
[2]	Albert R and Barabási A L 2002 Rev. Mod. Phys. 74 47
[3]	Adamic L A, Huberman B A, Barabási A L, Albert R, Jeong H and Bianconi G 2000 Science 287 5461
[4]	Dorogovtsev S N and Mendes J F F 2002 Adv. Phys. 51 1079
[5]	Roger G, Alex A, Albert D G, Francesc G 2002 Phys. Rev. E 66 026704
[6]	Onuttom N and Iraj S 2010 Phys. Rev. E 82 036102
[7]	Watts D J and Strogatz S H 1998 Nature 393 440
[8]	Newman M E J 2003 SIAM Rev. 45 167
[9]	Newman M E J 2001 Phys. Rev. E 64 016131
[10]	Newman M E J 2001 Phys. Rev. E 64 016132
[11]	Williams R J and Martinez N D 2000 Nature 404 180
[12]	Barbosa L A, Silva A C and Silva J K L 2006 Phys. Rev. E 73 041903
[13]	Otto S B, Rall B C and Brose U 2007 Nature 450 1226
[14]	Saldaña J 2007 Phys. Rev. E 75 027102
[15]	Barabási A L, Albert R and Jeong H 1999 Physica A 272 173
[16]	Slater J L, Hughes B D, Landman K A 2006 Phys. Rev. E 73 066111
[17]	Sarshar N and Roychowdhury V 2004 Phys. Rev. E 69 026101
[18]	Moore C, Ghoshal G and Newman M E J 2006 Phys. Rev. E 74 036121
[19]	Garcia-Domingo J L, Juher D and Salda?na J 2008 Physica D 237 640
[20]	Ben-Naim E and Krapivsky P L 2007 J. Phys. A: Math. Theor. 40 8607
[21]	Zhang X J, He Z S, He Z and Lez R B 2012 Physica A 391 3350
[22]	Zou Z Y, Liu P, Lei L and Gao J Z 2012 Chin. Phys. B 21 028904
[23]	Tian L X, He Y H, Huang Y 2012 Acta Phys. Sin. 61 228903 (in Chinese)
[24]	Ren X Z, Yang Z M, Wang B H and Zhou T 2012 Chin. Phys. Lett. 29 038904
[25]	Wang X W, Yang G H, Li X L and Xu X J 2013 Chin. Phys. B 22 018903
[26]	Yang G Y and Liu J G 2014 Chin. Phys. B 23 018901
[27]	Zhang X J, He Z and Lez R B 2016 J. Stat. Phys. 162 842
[28]	Wang J R, Wang J P, He Z and Xu H T 2015 Chin. Phys. B 24 060101
[29]	Xu R J, He Z, Xie J R and Wang B H 2016 Physica A 445 231
[30]	Krapivsky P L, Redner S and Leyvraz F 2000 Phys. Rev. Lett. 85 4629
[31]	Dorogovtsev S N, Mendes J F F and Samukhin A N 2000 Phys. Rev. Lett. 85 4633

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Degree distribution of random birth-and-death network with network size decline

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