Degree distribution of random birth-and-death network with network size decline
In this paper,we provide a general method to obtain the exact solutions of the degree distributions for random birthand-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 i...
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| Published in | Chinese physics B Vol. 25; no. 6; pp. 71 - 77 |
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| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
01.06.2016
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| Subjects | |
| Online Access | Get full text |
| ISSN | 1674-1056 2058-3834 1741-4199 |
| DOI | 10.1088/1674-1056/25/6/060202 |
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| Abstract | In this paper,we provide a general method to obtain the exact solutions of the degree distributions for random birthand-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. |
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| AbstractList | In this paper,we provide a general method to obtain the exact solutions of the degree distributions for random birthand-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. 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 greater than or equal to 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. |
| Author | 张晓军 杨会兰 |
| AuthorAffiliation | School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu 611731, China |
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| CitedBy_id | crossref_primary_10_1088_1674_1056_aba9c0 crossref_primary_10_1016_j_physa_2022_128244 crossref_primary_10_1088_1674_1056_ac3d82 crossref_primary_10_1109_TSMC_2023_3268372 crossref_primary_10_1142_S0217984918501592 crossref_primary_10_7498_aps_65_230201 crossref_primary_10_1142_S0217984917501615 |
| Cites_doi | 10.1126/science.286.5439.509 10.1103/PhysRevE.64.016131 10.1007/s10955-016-1447-6 10.1038/nature06359 10.1038/35004572 10.1103/PhysRevLett.85.4633 10.1103/PhysRevE.75.027102 10.1137/S003614450342480 10.1016/j.physd.2007.10.012 10.1103/PhysRevE.74.036121 10.1103/PhysRevE.73.066111 10.1038/30918 10.1016/S0378-4371(99)00291-5 10.1103/PhysRevLett.85.4629 10.1016/j.physa.2012.01.040 10.1103/PhysRevE.69.026101 10.1080/00018730110112519 10.1103/PhysRevE.66.026704 10.1126/science.287.5461.2115a 10.1103/PhysRevE.64.016132 10.1103/RevModPhys.74.47 10.1103/PhysRevE.73.041903 10.1088/1751-8113/40/30/001 10.1016/j.physa.2015.10.002 |
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| Notes | random birth-and-death network（RBDN）;Markov chain;generating function;degree distribution Xiao-Jun Zhang,Hui-Lan Yang In this paper,we provide a general method to obtain the exact solutions of the degree distributions for random birthand-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. 11-5639/O4 ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 23 |
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| References | Onuttom N (6) 2010; 82 27 29 Wang J R (28) 2015; 24 Barábasi A L (1) 1999; 286 30 Yang G Y (26) 2014; 23 31 10 11 12 Ben-Naim E (20) 2007; 40 13 14 15 16 17 18 19 Ren X Z (24) 2012; 29 Wang X W (25) 2013; 22 2 3 4 5 7 8 9 Tian L X (23) 2012; 61 Zou Z Y (22) 2012; 21 21 |
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| Snippet | In this paper,we provide a general method to obtain the exact solutions of the degree distributions for random birthand-death network（RBDN） with network size... 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... |
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| SubjectTerms | Computer simulation Exact solutions Mathematical analysis Mathematical models Networks Steady state Stochastic processes Transformations 变换方程 度分布 死亡 求解过程 网络规模 节点计算 计算机仿真 随机过程 |
| Title | Degree distribution of random birth-and-death network with network size decline |
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