一类修正Cooper-Frieze网络的稳定性研究

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基金项目: 国家自然科学基金资助项目(10671212);高校博士点基金资助项目(20050533036)

Markov Chain-Based Stability Analysis of a Modified Cooper-Frieze Model

1.
School of Mathematics, Central South University, Changsha 410075, P. R. China;

摘要: 基于Markov链理论，研究了一类修正Cooper-Frieze模型的稳定性．通过将模型中节点度与Markov链建立联系，利用Markov理论中首达概率的思想为稳态度分布的存在性提供了证明，并从数学上推导出度分布的具体表达式．最后，对该模型的度分布和聚集性提供了仿真分析, 并与BA模型作了相应的对比．
- 增长网络 /
- 择优连接 /
- 幂率分布
Abstract: From the perspective of probability,the stability of a modified Cooper-Frieze model is studied.Based on the concept and technique of first-passage probability in Markov theory,a rigorous proof for existence of the steady-state degree distribution was provided,moreover the explicit formula was derived analytically.Finally,extensive numerical simulations of the model,including the degree distribution and the clustering were performed.
- growing networks /
- preferential attachment /
- power law

[1]	Barabsi A L, Albert R, Jeong H. Mean-field theory for scale-free random networks[J].Physica A,1999,272(1):173-187. doi: 10.1016/S0378-4371(99)00291-5
[2]	Bollobs B,Riordan O M, Spencer J,et al.The degree sequence of a scale-free random graph process[J].Random Structures and Algorithms,2001,18(3):279-290. doi: 10.1002/rsa.1009
[3]	Albert R, Barabsi A L. Topology of evolving networks:local events and universality[J].Physical Review Letters,2000,85(24):5234-5237. doi: 10.1103/PhysRevLett.85.5234
[4]	CHEN Qing-hua,SHI Ding-hua.The modeling of the scale-free networks[J].Physica A,2004,335(1):240-248. doi: 10.1016/j.physa.2003.12.014
[5]	Cooper C, Frieze A.A general model of web graphs[J].Random Structures and Algorithms,2003,22(3):311-335. doi: 10.1002/rsa.10084
[6]	Hou Z T, Kong X X, Shi D H,et al.Degree-distribution stability of scale-free networks[A].arXiv:0805.1434v1[math PR]. ,2008.
[7]	Barabsi A L,Albert R.Emergence of scaling in random networks[J].Science,1999,286(5439):509-512. doi: 10.1126/science.286.5439.509
[8]	Stolz O.Vorlesungen ber Allgemeine Arithmetik[M].Leipzig:Teubner,1885.
[9]	Watts D J, Strogatz S H. Collective dynamics of small-world networks[J].Nature,1998,393(6684):440-442. doi: 10.1038/30918