 Spectral properties of Supra-Laplacian for partially interdependent networksYong Yang, Lilan Tu, Tianjiao Guo and Jiabo Chen Applied Mathematics and Computation, 2020, vol. 365, issue C Abstract: The spectrum of the Laplacian matrices of complex networks is a key factor in network functionality. In this paper, the spectral properties of Supra-Laplacian for partially interdependent networks are investigated. Based on Matrix Perturbation Theory, refined results of the eigenvalue properties of Laplacian matrices are provided, which shows that the size relationship of the first-order approximate solutions of the eigenvalues remains unchanged, even if there is perturbation. Using these results, the theoretical approximate formulae of the minimum non-zero eigenvalue and the maximum eigenvalue of Supra-Laplacian for partially interdependent networks are derived, respectively. The outcomes in this paper are more general and need fewer calculations than that in the literature [13,14]. Finally, the simulations and applications of synchronizability and diffusion process verify the feasibility and effectiveness of the proposed solutions. The findings can be instructive for networks when linking to the spectral properties of the Supra-Laplacian. Keywords: Partially interdependent networks; Laplacian matrix; Matrix Perturbation Theory; Spectral properties (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:365:y:2020:i:c:s0096300319307325 DOI: 10.1016/j.amc.2019.124740 Access Statistics for this article Applied Mathematics and Computation is currently edited by Theodore Simos More articles in Applied Mathematics and Computation from Elsevier |
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