Identification of Network Topology Variations Based on Spectral Entropy

• Published in: IEEE transactions on cybernetics Vol. 52; no. 10; pp. 10468 - 10478
• Main Authors: Su, Housheng, Chen, Dan, Pan, Gui-Jun, Zeng, Zhigang
• Format: Journal Article
• Language: English
• Published: United States IEEE 01.10.2022; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Communicability matrix; Complex networks; Eigenvalues; Eigenvalues and eigenfunctions; Entropy; global topology; Information dissemination; Laplace equations; Network topologies; networks; Probability distribution; spectral entropy; Symmetric matrices; Topology
• ISSN: 2168-2267; 2168-2275
• DOI: 10.1109/TCYB.2021.3070080

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.