title: Laplacian spectra of a class of small-world networks and their applications.
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.
authors.affiliation: 1] School of Computer Science, Fudan University, Shanghai 200433, China [2] Shanghai Key Laboratory of Intelligent Information Processing, Fudan University, Shanghai 200433, China.
authors.forename: Hongxiao
authors.initials: H
authors.lastname: Liu
authors.affiliation: Theoretical Polymer Physics, University of Freiburg, Hermann-Herder-Str.3, D-79104 Freiburg, Germany.
authors.forename: Maxim
authors.initials: M
authors.lastname: Dolgushev
authors.affiliation: 1] School of Computer Science, Fudan University, Shanghai 200433, China [2] Shanghai Key Laboratory of Intelligent Information Processing, Fudan University, Shanghai 200433, China.
authors.forename: Yi
authors.initials: Y
authors.lastname: Qi
authors.affiliation: 1] School of Computer Science, Fudan University, Shanghai 200433, China [2] Shanghai Key Laboratory of Intelligent Information Processing, Fudan University, Shanghai 200433, China.
authors.forename: Zhongzhi
authors.initials: Z
authors.lastname: Zhang