Spectral analysis for a family of treelike networks

Meifeng Dai, Xiaoqian Wang, Yufei Chen, Yue Zong, Yu Sun and Weiyi Su

Physica A: Statistical Mechanics and its Applications, 2018, vol. 505, issue C, 1-6

Abstract: For a network, knowledge of its Laplacian eigenvalues is central to understand its structure and dynamics. In this paper, we study the Laplacian spectra and their applications for a family of treelike networks. Firstly, in order to obtain the Laplacian spectra, we calculate the constant term and monomial coefficient of characteristic polynomial of the Laplacian matrix for a family of treelike networks. By using the Vieta theorem, we then obtain the sum of reciprocals of all nonzero eigenvalues of Laplacian matrix. Finally, we determine some interesting quantities that are related to the sum of reciprocals of all nonzero eigenvalues of Laplacian matrix, such as Kirchhoff index, global mean-first passage time (GMFPT).

Keywords: Laplacian spectra; Treelike network; Kirchhoff index; Global mean-first passage time (search for similar items in EconPapers)
Date: 2018
References: View complete reference list from CitEc
Citations: View citations in EconPapers (3)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:505:y:2018:i:c:p:1-6

DOI: 10.1016/j.physa.2018.02.088

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