一类小世界网络的特征值研究

Study on the a Kind of Eigenvalues of Small World Network

研究了一类具有随机长连接强度的时滞小世界网络的特征值分布。首先给出小世界网络的结构和矩阵表示,分析了构成小世界网络的规则环形网络的连接强度矩阵的最大特征值、最小特征值和其他n-2个特征值的取值范围,讨论了小世界网络的长连接强度矩阵元素Xij的数学期望和方差,进而分析了小世界网络的长连接强度矩阵X的特征值分布,最后给出了小世界网络连接强度矩阵D的特征值分布。

A kind of eigenvalue distribution of a small world network with time delay with random long connection strength is studied.Firstly,the structure and matrix representation of small world network are given.The maximum eigenvalue,the minimum eigenvalue and the value range of other n-2 eigenvalues of the connection strength matrix of regular ring network of small world network are analyzed.The mathematical expectation and variance of the element Xij of the long connection strength matrix of small world network is discussed,then the eigenvalue distribution of the long connection strength matrix X of small world network is analyzed.Finally,the eigenvalue distribution of the connection strength matrix D of small world network is given.