一类生长树状网络的Laplacian谱和特征向量的递归解
Recursive solutions for Laplacian spectra and eigenvectors of a class of growing treelike networks
摘要：
复杂网络的拉普拉斯特征值和特征向量的完整知识在理解运行于其上的各种动力学过程中起着突出的作用;然而，解析地确定拉普拉斯特征值和特征向量是一个理论挑战。本文研究了一类确定性增长树状网络的Laplacian谱及其相应的特征向量。这两个有趣的量是通过从网络的结构导出的递归关系确定的。从严格的关系式出发，可以求出任意大小网络的完全本征值和本征向量。解析方法开辟了解析计算其他一些确定性网络的特征值和特征向量的途径，使其能够准确地计算其频谱特性。
英文摘要：
The complete knowledge of Laplacian eigenvalues and eigenvectors of complex networks plays an outstanding role in understanding various dynamical processes running on them; however, determining analytically Laplacian eigenvalues and eigenvectors is a theoretical challenge. In this paper, we study the Laplacian spectra and their corresponding eigenvectors of a class of deterministically growing treelike networks. The two interesting quantities are determined through the recurrence relations derived from the structure of the networks. Beginning from the rigorous relations one can obtain the complete eigenvalues and eigenvectors for the networks of arbitrary size. The analytical method opens the way to analytically compute the eigenvalues and eigenvectors of some other deterministic networks, making it possible to accurately calculate their spectral characteristics.
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