加权迭代六边形网络的谱分析

Spectral Analysis of Weighted Iterative Hexagonal Networks

网络的结构特性和动态方面的许多信息是由标准拉普拉斯谱来衡量的.文章建立了一类加权迭代六边形网络,基于网络的自相似结构探寻标准邻接矩阵的特征值和特征向量在相邻两代之间的递推关系,得到标准邻接矩阵特征值的解析式,最后根据标准邻接矩阵和标准拉普拉斯矩阵的联系,得到加权迭代六边形网络的标准拉普拉斯谱的结构式.

Much information about the structural properties and dynamical aspects of a network is measured by the normalized Laplacian spectrum.The paper constructs a weighted iterative hexagonal networks,explores the recursive relationship between the eigenvalues and eigenvectors of the normalized adjacency matrix in two adjacent generations based on the self-similar structure of the network,and obtains the analytic formula of the eigenvalues of the normalized adjacency matrix.Finally the structural formula of the normalized Laplacian spectrum of the weighted iterative hexagonal networks is obtained according to the connection between the normalized adjacency matrix and the normalized Laplacian matrix.