文档介绍：南京航空航天大学硕士学位论文
摘要
复杂网络近年来在国内外掀起了研究的热潮,受到来自科学与工程各个领域研究者的强烈
关注。现实世界中的许多系统都可以通过复杂网络进行描述,例如:社会网、万维网、因特网
等。从数学的角度看,任何一个网络都可以抽象为一个由点集 V 和边集 E 构成的图,其中,结
点代表网络中的元素,边代表个体间的关联性。许多网络演化模型都可以被看作状态空间是图
集的马尔可夫过程。与经典随机图过程不同,图值随机过程研究节点和边都随机变化的图过程。
这里,随时间的变化,节点的增加和删除是随机的,在删除节点的同时也删除该节点所连接的
边。图值过程的团聚性是人们感兴趣的一个主要性质,特别是具有这种特性的图值过程满足的
充分条件,更是引起人们极大的关注。为了搞清复杂网络特征的形成机制,研究人员提出了众
多的网络演化模型。然而,到目前为止,对于图值过程演化模型的特征研究大都停留在数值仿
真或是平均场,主方程等统计物理的方法,有些模型缺乏数学上的严格性。本文研究具有加点
加边机制的图值马氏过程,从随机分析角度出发,给出这类图值马氏过程不具有大团聚性的一
个充分条件。
关键词:复杂网络,图值马氏过程,团聚系数,确定性连接,无标度性
I
一类图值过程不具有大团聚性的一个充分条件
Abstract
In recent years, works have set off a wave of domestic and foreign research, and
have been strongly concerned by the researchers in all areas from the science and engineering. Many
real world systems can be described works, such as works, the World Wide
Web, the and so on.. From the mathematical point of view, work can be
abstracted as a graph consisting of node-set V and edge-set E, where nodes represent
the elements of work and edges represent the relationship between elements.
Many work models can be viewed as graph-valued Markov processes.
Different from the classical random graph process, graph-valued stochastic process discusses the
graph process where nodes and edges vary randomly. Here, add and remove nodes randomly over the
time, when a node is removed, the edges linking to it are also removed. The scale-free behavior for
the high clustering property of the graph-valued process are the main property that people are
interested in, especially the sufficient condition for graph-valued process possessing the property
really catches researchers’ attention. To find out features of the formation mechanism plex
networks, researches have propose many models of works. However, up to date, the
features researches of graph-valued process of evolution models have been remained mostly in
numerical simulation or the mean-field theory an