Spectral analysis for weighted tree-like fractals

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

Physica A: Statistical Mechanics and its Applications, 2018, vol. 492, issue C, 1892-1900

Abstract: Much information about the structural properties and dynamical aspects of a network is measured by the eigenvalues of its normalized Laplacian matrix. In this paper, we aim to present a study on the spectra of the normalized Laplacian of weighted tree-like fractals. We analytically obtain the relationship between the eigenvalues and their multiplicities for two successive generations. As an example of application of these results, we then derive closed-form expressions for their multiplicative Kirchhoff index and Kemeny’s constant.

Keywords: Normalized Laplacian spectrum; Kirchhoff index; Kemeny’s constant (search for similar items in EconPapers)
Date: 2018
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:492:y:2018:i:c:p:1892-1900

DOI: 10.1016/j.physa.2017.11.105

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