复杂网络统计力学的差分方程方法

郭进利

doi:10.3879/j.issn.1000-0887.2009.08.013

复杂网络统计力学的差分方程方法

doi: 10.3879/j.issn.1000-0887.2009.08.013

郭进利

上海理工大学管理学院,上海 200093

基金项目: 国家自然科学基金资助项目(70871082);上海市重点学科建设资助项目(S30504)

详细信息

作者简介:
郭进利(1960),男,陕西人,教授,博士(E-mail:phd5816@163.com).

中图分类号: N94;TP1;TP3
计量
- 文章访问数: 1381
- HTML全文浏览量: 180
- PDF下载量: 921
- 被引次数: 0
出版历程
- 收稿日期: 2008-06-13
- 修回日期: 2009-06-08
- 刊出日期: 2009-08-15

Difference Equation Approach of Statistical Mechanics of Complex Networks

GUO Jin-li

Business School, University of Shanghai for Science and Technology, Shanghai 200093, P. R. China

摘要

摘要: 通过分析几种估计增长网络度分布方法的缺点，提出估计度分布的差分方程方法，不仅避免了复杂网络分析中将离散问题连续化带来的逻辑矛盾，也避免了网络稳态度分布存在性的假设．利用这个方法给出Poisson增长择优连接网络的度分布公式，借助Poisson过程理论和Gamma分布的性质严格证明Poisson增长择优连接网络是无标度网络．
- 复杂网络 /
- 度分布 /
- 无标度网络
Abstract: The difference equation approach of estimating degree distribution in growing networks was proposed after analyzing the disadvantages of some existing approaches. This approach avoids not only logic conflicts brought by continuum of discrete problem, but also the assumption of existence of the stationary degree distribution in network analysis. The degree distribution formula of Poisson growth and preferential attachment network was obtained by this approach. It was strictly proved that this network is scale free based on Poisson process theory and properties of Gamma distribution.
- complex network /
- degree distribution /
- scale free network

HTML全文

参考文献(22)

[1]	Erds P, Rényi A. On random graphs[J].Publicationes Mathematicae,1959,6:290-297.
[2]	Price D J D. Networks of scientific paper[J].Science,1965,149(3683):510-515. doi: 10.1126/science.149.3683.510
[3]	Price D J D. A general theory of bibliometric and other cumulative advantage processes [J].J Amer Soc Inform Sci,1976,27(5):292-306. doi: 10.1002/asi.4630270505
[4]	Watts D J, Strogatz S H. Collective dynamics of “small-world”networks[J].Nature,1998,393(6):440-442. doi: 10.1038/30918
[5]	Barabási A L, Albert R. Emergence of scaling in random networks[J].Science,1999,286(5439):509-512. doi: 10.1126/science.286.5439.509
[6]	Barabási A L, Albert R, Jeong H. Mean-field theory for scale-free random networks[J]. Physica A,1999,272(1/2):173-187. doi: 10.1016/S0378-4371(99)00291-5
[7]	Albert R, Barabási A L. Statistical mechanics of complex networks[J].Rev Mod Phys,2002,74(1):47-97. doi: 10.1103/RevModPhys.74.47
[8]	Boccaletti S, Latora V, Moreno Y,et al.Complex networks:structure and dynamics[J].Physics Reports,2006,424(4/5):175-308. doi: 10.1016/j.physrep.2005.10.009
[9]	Krapivsky P L, Redner S. Organization of growing random networks[J].Phys Rev E,2001,63(6):066123-1—066123-14. doi: 10.1103/PhysRevE.63.066123
[10]	Dorogovtsev S N, Mendes J F F.Evolution of Networks:From Biological Nets to the Internet and WWW[M].Oxford UK:Oxford University Press, 2003.
[11]	Toivonen R, Onnela J P, Saramki J,et al.A model for social networks[J].Physica A,2006,371(2):851-860. doi: 10.1016/j.physa.2006.03.050
[12]	Wang L N, Guo J L, Yang H X，et al.Local preferential attachment model for hierarchical networks[J].Physica A,2009,388(8):1713-1720. doi: 10.1016/j.physa.2008.12.028
[13]	Guo J L, Bai Y Q. A note on mean-field theory for scale-free random networks, dynamics of continuous[J].Dynamics of Continuous, Discrete and Impulsive Systems, Ser B,2006,13(3):523-531.
[14]	Hase M O, Mendes J F F. Solvable metric growing networks[J].J Stat Mech,2008, P12002.doi: 10.1088/1742-5468/2008/12/P12002.
[15]	GUO Jin-li. The classification and analysis of dynamic networks[J].Chinese Physics, 2007,16(5):1239-1245. doi: 10.1088/1009-1963/16/5/012
[16]	Lü J H, Chen G, Cheng D. A time-varying complex dynamical network model and its controlled synchronization criteria[J].IEEE Trans Auto Contr,2005,50(6):841-846. doi: 10.1109/TAC.2005.849233
[17]	Chen L, Lü J H, Lu J L,et al.Local asymptotic coherence of time-varying discrete ecological networks[J].Automatica,2009,45(2):546-552. doi: 10.1016/j.automatica.2008.09.006
[18]	Yu W W, Chen G R, Lü J H. On pinning synchronization of complex dynamical networks[J]. Automatica,2009,45(2):429-435. doi: 10.1016/j.automatica.2008.07.016
[19]	郭进利. 探讨动态复杂网络的新途径[J]. 系统工程理论与实践，2006，26(7):34-40.
[20]	Guo J L, Wang C P. Poisson continuous time growing complex networks[J].Dynamics of Continuous, Discrete and Impulsive Systems, Ser A,2006,13:970-972.
[21]	Ross S M.Stochastic Processes[M].New York:John Wiley & Sons,Inc,1983.
[22]	Bollobás B, Riordan O M. Mathematical results on scale-free random graphs[A].In:Handbook of Graphs and Network[C].Weinheim:Wiley-VCH, 2003, 1-34.