网络的生成及其结构分析

发布时间：2018-07-22 14:26

【摘要】：近年来，随着ER随机网络、WS小世界网络、BA无标度网络等模型的提出，网络生成模型的研究得到了大量的关注，特别是网络的生长及其拓扑结构研究，成为这一领域的研究的热点，人们开始关注更加复杂的网络结构。本文研究了社团结构的生成网络模型，发现与随机选择或社团度优先选择机制相比，社团之间采取社团平均度优先选择更符合实际；在此基础上，研究了疾病传播与生成网络模型关系。本文主要工作： 1.考虑了社团平均度优先选择机制，对其做了明确的定义，建立了社团度优先选择的生成网络模型。其中社团内部节点之间依然采取度优先连接机制，社团之间则采取社团平均度优先选择机制，进而利用平均域的方法对该模型进行理论分析，得到了该模型的节点度及其度分布，结果表明此网络符合无标度网络的特性，并对其进行数值模拟。 2.考虑了疾病传播与网络生成问题，，建立了适用于具有某种特殊性质的地方性传染病传播的生成网络模型。并对处于不同状态的易感者和染病者节点进行理论分析，分别得到每一时刻的易感者与感染者的度及其度分布。
[Abstract]:In recent years, with the development of ER random networks and small world networks such as scale-free networks, the research of network generation model has attracted a lot of attention, especially the research of network growth and topology structure. People begin to pay attention to the more complex network structure as the research focus in this field. In this paper, the network model of community structure is studied, and it is found that compared with random selection or degree of association preference, it is more practical to choose the average degree of community among communities. The relationship between disease transmission and generation network model is studied. The main work of this paper is as follows: 1. In this paper, the mechanism of community average preference is considered, and its definition is given, and the generating network model of community degree preference is established. Among them, the degree first connection mechanism is still adopted among the nodes within the community, and the average degree preference mechanism is adopted among the communities, and then the model is theoretically analyzed by using the mean domain method. The node degree and its degree distribution of the model are obtained. The results show that the network accords with the characteristics of scale-free network, and the numerical simulation is carried out. 2. In this paper, the problem of disease transmission and network generation is considered, and a generation network model suitable for the transmission of endemic infectious diseases with some special properties is established. The nodes of susceptible and infected persons in different states were analyzed theoretically, and the degree and distribution of susceptible and infected persons at each moment were obtained respectively.
【学位授予单位】：中北大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：O157.5

【共引文献】