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
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- 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

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参考文献(22)

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