加权koch网络多重分形分析和时序网络中节点重要性评估方法

发布时间：2018-06-09 00:34

本文选题：加权网络 + 多重分形分析　；参考：《湘潭大学》2017年硕士论文

【摘要】：本文的研究对象为加权网络和时序网络,这两类网络是无权网络的推广。在讨论加权网络时,本文关注的是分形和多重分形性质的分析,在讨论时序网络时,本文则讨论的是这类网络上节点重要性的评估方法。近些年来,加权网络因为它能更好刻画现实复杂系统的结构特性而受到很多研究者的关注,有关加权网络的结构研究中,涉及到加权网络多重分形性质方面的研究工作比较少。在本文中,受到Koch网络和Koch岛分形的启发,一种新型加权Koch网络模型被提出来作为研究加权网络的模型框架,随后本文从拓扑特性和特征值谱方面研究了这种新型加权Koch网络,接着本文重点研究了新型加权Koch网络的分形和多重分形特性,本文发现新提出的网络是分形网络并且具有多重分形测度,随后这些研究方法被应用来研究几个实际复杂网络,研究结果表明实际的加权复杂网络也具有无权复杂网络的一些类似拓扑性质,但是这两类网络的这些性质之间没有必然联系。受到数据的驱动以及各种应用的需求,时序网络中节点重要性的评估这一问题受到越来越多的学者关注。传统的方法主要针对的是静态网络,而且在分析这类问题时过多考虑了网络的拓扑特性,而对节点的动力学特性关注太少。本文主要关注网络节点的动力学特性,并把静态网络中的动态敏感中心性指标推广到时序网络,在三个实际网络数据数据集和一个理论网络数据集上建立SIR模型仿真,实验表明本文推广的方法比一些静态网络中常用的指标如度中心性、接近中心性、介数中心性以及它们的在时序网络中的推广指标都要准确。最后,作为一个应用,所推广的动态敏感中心性指标被用来研究节点的时序因素对时序网络传播行为的影响,结果表明网络节点的拓扑特性和时序都会对传播造成影响,而且当网络传播率β接近网络的传播阈值βc时,时序因素产生的影响将变小。
[Abstract]:The research object of this paper is weighted network and time series network, which are the extension of weighted network. In discussing weighted networks, this paper focuses on the analysis of fractal and multifractal properties, and discusses the evaluation methods of node importance in time series networks. In recent years, many researchers have paid attention to weighted networks because they can better describe the structural characteristics of complex systems in reality. In the study of weighted networks, there are few researches on multifractal properties of weighted networks. In this paper, inspired by Koch network and Koch island fractal, a new weighted Koch network model is proposed as a model framework to study the weighted network, and then this new weighted Koch network is studied in terms of topological characteristics and eigenvalue spectrum. Then the fractal and multifractal properties of the new weighted Koch network are studied. It is found that the new network is a fractal network and has multifractal measures. Then these methods should be used to study several real complex networks. The results show that the actual weighted complex networks also have some similar topological properties of unweighted complex networks, but there is no necessary relation between these properties of these two kinds of networks. Driven by data and required by various applications, the importance of nodes in time series networks has attracted more and more attention. The traditional method is mainly aimed at static network, and the topology of the network is considered too much when analyzing this kind of problem, but little attention is paid to the dynamic characteristics of nodes. This paper mainly focuses on the dynamic characteristics of network nodes, and extends the dynamic sensitivity center index of static network to time series network, and establishes Sir model simulation on three actual network data sets and one theoretical network data set. The experiments show that the proposed method is more accurate than some commonly used indexes in static networks such as degree centrality, proximity centrality, intermediate centrality and their generalization indexes in time series networks. Finally, as an application, the extended dynamic sensitivity centrality index is used to study the influence of the timing factors of nodes on the propagation behavior of time series networks. The results show that the topological characteristics and timing of network nodes will have an impact on the propagation. Moreover, when the network propagation rate 尾 is close to the network propagation threshold 尾 c, the influence of time series factors will be reduced.
【学位授予单位】：湘潭大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O157.5

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