Spectra And Coherence Analysis On Four Classes Of Weighted Networks

In this dissertation,we introduce four kinds of networks which are weighted small-world networks,weighted tree-like polymer networks,weighted hypercube and weighted folded hypercube networks and give several different and new methods to calculate Laplacian spectra.According to the relationship between the network coherence and laplacian spectra,the exact or approximate expression of the first-and second-order network coherence about these four kinds of networks are calculated for the first time,and the four results of network coherence are presented and analyzed intuitively by charts that obtained by numerical simulation.Content in this article is arranged as follows.In Chapter 1,we mainly introduce the development background and processes of complex networks and weighted networks,and give the definition of the first-and second-order network coherence and research situation at home and abroad which are the core content of this paper.In Chapter 2,we study the coherence of weighted small-world networks.We firstly introduce a class of weighted small-world network and obtain the laplaciam spectra by using determinant transformation and recursive relationship.Then,according to the definition of network coherence of this kind of weighted small-world network,the firstand second-order network coherence are calculated.Finally,the relationships between the network coherence and the relevant quantities are obtained and showed by numerical simulation intuitively.In Chapter 3,we focus on weighted tree-like polymer networks and analyse the first-and second-order network coherence.The Laplaciam spectra of the weighted networks are also calculated by using the determinant correlation property,and the coherence of the weighted tree-like polymer network is finally obtained by summing the sequence which follow the calculation methods of the previous chapter,but the calculation process is simplified.In Chapter 4,we introduce the weighted hypercube which Laplacian spectra is given in the form of lemma by using the method of induction.Then,the approximate expressions of the first-and second-order network coherence are obtained by use ofsqueeze theorem,so as to avoid the tedious process of calculating.The method of calculating spectra and network coherence are further optimized.In Chapter 5,the weighted folded hypercube is constructed by adding edges based on the networks of chapter 4,which is an extension of the weighted hypercube networks.In this chapter,we use reverse thinking that first summarize the conclusion,then obtain the Laplacian spectra of the networks by using mathematical induction.Finally,we obtain the approximate expressions of the first-and second-order network coherence by using the squeeze theorem.This chapter not only inherits the advantages of the previous chapter in the calculation method of network coherence,but also creates new solutions in the calculation of spectra,which further deepens the research.