Spectral Analysis And Application On Three Classes Of Tree-like Networks

In this dissertation,we study a performance index of three kinds of tree-like networks: eigentime identity on un-weighted fractal tree-like networks,weighted Cayley networks,un-weighted polymer networks for the first time.A method is created to calculate the laplacian spectra of un-weighted fractal tree-like networks and un-weighted Cayley networks.First-order network coherence on weighted Cayley networks is calculated for the first time.Content in this article is arranged as follows.In Chapter 1,we introduce the development processes and the basic concepts of complex networks and weighted networks.In Chapter 2,un-weighted polymer networks,weighted Cayley networks and un-weighted fractal tree-like networks are introduced.An important performance indicator-eigentime identity measuring the efficiency of information transmission on the network with stationary distribution is studied.Finally,eigentime identity on those three networks are obtained by using the relationship between normalized Laplacian spectra and eigentime identity.In Chapter 3,we focus on several performance indicators,such as,Kirchoff index,entire mean-first passage time(EMFPT)on un-weighted fractal tree-like networks and EMFPT on un-weighted Cayley networks.Several performance indicators on those two networks are obtained by using Laplacian spectra and the relationship between Laplacian spectra and and those performance indicators.In Chapter 4,a performance indicator-first-order network coherence measuring the ability to converge on the network is studied.Analytic expression of the performance indicator is obtained by using the relationship between Laplacian spectra,vieta theorem and this performance indicator.