随机行走在复杂网络上的交通行为特性分析

发布时间：2018-05-29 14:21

本文选题：随机行走 + 复杂网络　；参考：《合肥工业大学》2015年硕士论文

【摘要】：近年来,复杂网络的研究受到科学界的普遍关注,它的研究对了解现实生活中的网络、系统具有重要的意义。研究复杂网络的一个重要课题是通过研究网络上的交通动力学特性来了解网络的性质,从而进一步了解真实网络的功能。关于交通动力学特性的研究,学者们也提出了很多的研究方法,本文是通过随机行走模型来探索复杂网络的网络特性。随机行走模型简便,且最大限度的涵盖了许多现实生活中的交通过程,例如疾病传播,交通运输,网络搜索等。本文主要工作如下。(1)研究了一般无权网络上随机行走的交通动力学特性。通过对在一般网络上随机行走性质的分析,结合图谱理论的相关知识,用更为简洁的计算方法给出平均首到达时间(MFPT)的精确解。进一步根据利用柯西不等式对解析结果的处理,通过计算机仿真对MFPT与网络结构性质之间的关系进行了呈现。(2)研究了加权确定型无标度小世界网络上随机行走的交通动力学特性。对含有一个陷阱节点的加权确定型无标度小世界网络上的随机行走问题进行了研究。给出了首到达时间(FPT)随着网络结构变化的演化关系式进而对平均吸收时间(ATT)进行了求解。结果显示ATT随着网络规模的增大呈超线性增长。(3)研究了度不相关加权网络上随机行走的交通动力学特性。对两种不同类型的随机行走在度不相关加权网络上的静态分布函数进行了求解,进一步给出了随机行走过程的重要特性分析指标首次返回时间(MFRT)的解析解,并通过计算机仿真对结果进行了验证。(4)研究了加权网络上随机行走覆盖时间的特性。网络覆盖时间特性的研究具有很高的现实研究意义。本文通过计算机仿真呈现了加权网络上不同随机行走规则下网络边或节点的遍历效率,呈现出了网络结构特性对遍历效率的影响关系。
[Abstract]:In recent years, the research of complex network has been paid more and more attention by the scientific community. It is of great significance to understand the network and system in real life. An important task in the study of complex networks is to understand the properties of networks by studying the characteristics of traffic dynamics on the networks, so as to further understand the functions of real networks. As for the study of traffic dynamics, many research methods have been proposed. In this paper, the random walk model is used to explore the network characteristics of complex networks. The random walk model is simple and covers many real life traffic processes, such as disease transmission, transportation, network search and so on. The main work of this paper is as follows. By analyzing the properties of random walk on general networks and combining with the relevant knowledge of map theory, the exact solution of average first arrival time (MFPTT) is obtained by a more concise calculation method. Further, according to the treatment of analytic results by using Cauchy inequality, The relationship between MFPT and network structure is presented by computer simulation. (2) the traffic dynamics characteristics of random walk on a weighted scale-free small-world network are studied. The random walk problem on a weighted deterministic scale-free small-world network with a trap node is studied. The evolution relation of the first arrival time (FPTT) with the change of network structure is given and the average absorption time (ATT) is solved. The results show that ATT increases superlinearly with the increase of network size. The static distribution function of two different types of random walks on a weighted network is solved, and the analytical solution of the first return time (MFRTT) of the important characteristic analysis index of the random walk process is given. The results are verified by computer simulation. (4) the characteristics of random walk coverage time on weighted networks are studied. The study of network coverage time is of great practical significance. In this paper, the ergodic efficiency of the network edge or node under different random walking rules on the weighted network is presented by computer simulation, and the relationship between the network structure characteristics and the ergodic efficiency is presented.
【学位授予单位】：合肥工业大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：U491

【相似文献】