Laplacian spectra of a class of small-world networks and their applications

Scientific Reports
Hongxiao LiuZhongzhi Zhang

Abstract

One of the most crucial domains of interdisciplinary research is the relationship between the dynamics and structural characteristics. In this paper, we introduce a family of small-world networks, parameterized through a variable d controlling the scale of graph completeness or of network clustering. We study the Laplacian eigenvalues of these networks, which are determined through analytic recursive equations. This allows us to analyze the spectra in depth and to determine the corresponding spectral dimension. Based on these results, we consider the networks in the framework of generalized Gaussian structures, whose physical behavior is exemplified on the relaxation dynamics and on the fluorescence depolarization under quasiresonant energy transfer. Although the networks have the same number of nodes (beads) and edges (springs) as the dual Sierpinski gaskets, they display rather different dynamic behavior.

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Citations

Sep 17, 2016·The Journal of Chemical Physics·Mircea Galiceanu, Aurel Jurjiu
Jan 10, 2017·Scientific Reports·Elena Agliari, Flavia Tavani
Mar 1, 2018·Scientific Reports·Aurel JurjiuMircea Galiceanu
Jan 20, 2018·Soft Matter·Jonas Grimm, Maxim Dolgushev
Jul 15, 2015·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Zhongzhi ZhangXiaoye Guo
Apr 15, 2016·Physical Review. E·Hongxiao LiuZhongzhi Zhang
Apr 1, 2018·Chaos·Meifeng DaiWeiyi Su
Oct 3, 2015·Physical Review Letters·Nikolaj KulvelisOliver Mülken
Apr 10, 2019·Polymers·Aurel Jurjiu, Mircea Galiceanu
Sep 3, 2017·Chaos·Junhao Peng, Elena Agliari

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