A Vertex-Number-Evolving Markov Chain of Networks

被引：2

作者：

Shi, Dinghua ^{[2
]}

Xu, Hong ^{[2
]}

Liu, Liming ^{[1
]}

机构：

[1] Hong Kong Polytech Univ, Dept Logist & Maritime Studies, Hong Kong, Hong Kong, Peoples R China

[2] Shanghai Univ, Dept Math, Shanghai 200444, Peoples R China

来源：

INTERNATIONAL CONFERENCE ON COMPLEXITY AND INTERDISCIPLINARY SCIENCES: 3RD CHINA-EUROPE SUMMER SCHOOL ON COMPLEXITY SCIENCES | 2010年 / 3卷 / 05期

基金：

中国国家自然科学基金;

关键词：

scale-free network; BA model; LCD model; initial attraction model; vertex number with degree k; Markov chain; stability; convergence in probability;

D O I：

10.1016/j.phpro.2010.07.016

中图分类号：

O59 [应用物理学];

学科分类号：

摘要：

We have introduced a vector Markov chain of the vertex number with degree k in network evolving process as a framework of theoretical analysis and proved the stability of the BA-1 model and the LCD-1 model. In this paper, we use the vertex-number-evolving Markov chain to prove rigorously the existence of the steady-state degree distribution P(k) for a special case of the initial attraction model allowing multiple edges. The application of our approach to the LCD-m model, the result shows that it is more simpler than Bollobas' method.

引用

页码：1757 / 1765

页数：9

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