title: Geometrical invariability of transformation between a time series and a complex network.
abstract: We present a dynamically equivalent transformation between time series and complex networks based on coarse geometry theory. In terms of quasi-isometric maps, we characterize how the underlying geometrical characters of complex systems are preserved during transformations. Fractal dimensions are shown to be the same for time series (or complex network) and its transformed counterpart. Results from the Rössler system, fractional Brownian motion, synthetic networks, and real networks support our findings. This work gives theoretical evidences for an equivalent transformation between time series and networks.
authors.affiliation: Shenzhen Graduate School, Harbin Institute of Technology, Shenzhen, China.
authors.forename: Yi
authors.initials: Y
authors.lastname: Zhao
authors.affiliation: Shenzhen Graduate School, Harbin Institute of Technology, Shenzhen, China.
authors.forename: Tongfeng
authors.initials: T
authors.lastname: Weng
authors.affiliation: Mathematics and Physics Centre, Xi'an Jiaotong-Liverpool University, Suzhou, China and Mathematical Institute, University of Oxford, Oxford, United Kingdom.
authors.forename: Shengkui
authors.initials: S
authors.lastname: Ye
mesh_terms: D008962:Models, Theoretical; D009038:Motion; D013269:Stochastic Processes; D013997:Time Factors