title: From networks to time series.
abstract: In this Letter, we propose a framework to transform a complex network to a time series. The transformation from complex networks to time series is realized by the classical multidimensional scaling. Applying the transformation method to a model proposed by Watts and Strogatz [Nature (London) 393, 440 (1998)], we show that ring lattices are transformed to periodic time series, small-world networks to noisy periodic time series, and random networks to random time series. We also show that these relationships are analytically held by using the circulant-matrix theory and the perturbation theory of linear operators. The results are generalized to several high-dimensional lattices.
authors.affiliation: Graduate School of Science and Engineering, Saitama University, Sakura-ku, Saitama-shi, Saitama, Japan. yshimada@sat.t.u-tokyo.ac.jp
authors.forename: Yutaka
authors.initials: Y
authors.lastname: Shimada
authors.forename: Tohru
authors.initials: T
authors.lastname: Ikeguchi
authors.forename: Takaomi
authors.initials: T
authors.lastname: Shigehara
mesh_terms: D004463:Ecology; D008962:Models, Theoretical; D011210:Power Plants; D012944:Social Support