This paper constructs a new spectrum of networks by means of the matrix of link-state ofthe network,which can reveal the characteristics of the correlation between the degrees of the network.Also,the computation of th...This paper constructs a new spectrum of networks by means of the matrix of link-state ofthe network,which can reveal the characteristics of the correlation between the degrees of the network.Also,the computation of this spectrum of networks is usually more feasible and more efficient due tothe much lower order of its matrix of link-state than its adjacent matrix in practice.Some estimatesfor the bounds of the key eigenvalues in the spectrum are obtained,the corresponding inequalities arepresented and proved.For the sake of its application,the authors define spectrum of networks in twoways,and all theorems are given in parallel for both kinds of definition.In addition,the authors finda symmetry in the spectrum,which is relative to the characteristic of structure of its network to someextent.展开更多
基金supported by the Key Project for Fundamental Research of STCSM under Grant No. 06JC14057
文摘This paper constructs a new spectrum of networks by means of the matrix of link-state ofthe network,which can reveal the characteristics of the correlation between the degrees of the network.Also,the computation of this spectrum of networks is usually more feasible and more efficient due tothe much lower order of its matrix of link-state than its adjacent matrix in practice.Some estimatesfor the bounds of the key eigenvalues in the spectrum are obtained,the corresponding inequalities arepresented and proved.For the sake of its application,the authors define spectrum of networks in twoways,and all theorems are given in parallel for both kinds of definition.In addition,the authors finda symmetry in the spectrum,which is relative to the characteristic of structure of its network to someextent.
