三类加权网络上随机游走的平均加权首达时间

发布时间：2018-04-11 21:27

本文选题：平均加权首达时间 + 全局平均加权首达时间　；参考：《江苏大学》2017年硕士论文

【摘要】：为了更好的研究加权网络结构特征,我们需要研究加权网络的一个重要的物理性能—平均加权首达时间(MWFPT).本文主要研究和计算两类加权树状网络和一类加权分形网络上随机游走的平均加权首达时间,并研究其渐近行为的影响因素.具体来说,我们的工作如下:绪论主要介绍了加权网络的研究背景和目前的研究现状,并介绍了在加权网络上计算平均加权首达时间的常用到的一些基本概念.第二章介绍了一类加权树状网络,首次利用两种方法计算了在这类网络上随机行走的全局平均首达时间(EMWFPT).根据网络的结构特征,一方面计算中心节点的接收和发送时间,另一方面利用EMWFPT和平均加权最短路径之间的关系式,最后都得到EMWFPT渐近行为.结果表明,EMWFPT的主要项与网络规模大小成线性关系.第三章在无穷加权树状网络中,我们给出一个准确计算EMWFPT解析式的方法.这个方法是基于不同代中EMWFPT和Laplacian特征值之间的关系,计算中的关键步骤是求特征多项式的常数项和一次项的系数.最后,我们得到加权树状网络的EMWFPT解析式.结果表明,EMWFPT的主要项与网络规模的大小成超线性增长关系.第四章介绍了一类加权分形网络.在此类网络中我们首次引进修正盒维数的定义,对于它的存在性给予严格的证明.然后,理论证明了修正盒维数依赖于权重因子和复制数.接下来计算出此类网络的平均加权接收时间,结果显示陷阱点的有效性依赖于修正盒维数:盒维数越大,陷阱效率越高.
[Abstract]:In order to better study the characteristics of weighted network structure, we need to study one of the important physical properties of the weighted network, that is, average weighted first arrival time (WDOT) and MWFPTT.In this paper, we study and calculate the average weighted first arrival time of random walk on two kinds of weighted tree networks and a class of weighted fractal networks, and study the influencing factors of their asymptotic behavior.Specifically, our work is as follows: the introduction mainly introduces the research background and current research status of weighted networks, and introduces some basic concepts commonly used to calculate average weighted first arrival time on weighted networks.In the second chapter, a class of weighted tree networks is introduced. For the first time, two methods are used to calculate the global average first arrival time (EMWFPTT) of random walking on this kind of networks.According to the structural characteristics of the network, on the one hand, the reception and transmission time of the central node is calculated; on the other hand, by using the relationship between EMWFPT and the average weighted shortest path, the asymptotic behavior of EMWFPT is obtained.The results show that the main terms of EMWFPT are linearly related to the size of the network.In chapter 3, we give an accurate method to calculate the EMWFPT analytic formula in the infinite weighted tree network.This method is based on the relationship between EMWFPT and Laplacian eigenvalues in different generations. The key step in the calculation is to find the constant term and the coefficient of the first term of the characteristic polynomial.Finally, we obtain the EMWFPT analytic formula of weighted tree network.The results show that the main terms of EMWFPT are superlinearly increased with the size of the network.Chapter 4 introduces a class of weighted fractal networks.In this kind of network, we first introduce the definition of modified box dimension, and give a strict proof of its existence.Then, it is proved that the modified box dimension depends on the weight factor and the copy number.Then the average weighted reception time of the network is calculated. The results show that the validity of the trap point depends on the modified box dimension: the larger the box dimension, the higher the trap efficiency.
【学位授予单位】：江苏大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O157.5

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