Su Housheng, Chen Dan, Pan Gui-Jun, Zeng Zhigang
IEEE Trans Cybern. 2022 Oct;52(10):10468-10478. doi: 10.1109/TCYB.2021.3070080. Epub 2022 Sep 19.
Based on the fact that the traditional probability distribution entropy describing a local feature of the system cannot effectively capture the global topology variations of the network, some indicators constructed by the network adjacency matrix and Laplacian matrix come into being. Specifically, these measures are based on the eigenvalues of the scaled Laplace matrix, the eigenvalues of the network communicability matrix, and the spectral entropy based on information diffusion that has been proposed recently, respectively. In this article, we systematically study the dependence of these measures on the topological structure of the network. We prove from various aspects that spectral entropy has a better ability to identify the global topology than the traditional distribution entropy. Furthermore, the indicator based on the eigenvalues of the network communicability matrix achieves good results in some aspects while, overall, the spectral entropy is able to identify network topology variations from a global perspective.
基于传统的描述系统局部特征的概率分布熵无法有效捕捉网络的全局拓扑变化这一事实，一些由网络邻接矩阵和拉普拉斯矩阵构建的指标应运而生。具体而言，这些度量分别基于缩放拉普拉斯矩阵的特征值、网络可达性矩阵的特征值以及最近提出的基于信息扩散的谱熵。在本文中，我们系统地研究了这些度量对网络拓扑结构的依赖性。我们从各个方面证明，谱熵比传统分布熵具有更好的识别全局拓扑的能力。此外，基于网络可达性矩阵特征值的指标在某些方面取得了良好的结果，而总体而言，谱熵能够从全局角度识别网络拓扑变化。
