Research On Matrix Properties Of The Conversion Process From Complex Networks To Time Series

In this Internet age, to better study various types of complex networks has become an urgent demand. Time series is a good perspective to analyze complex networks, with the help of time series, we can not only quantitatively extract useful information in complex networks, but also effectively forecast. Therefore,the realization of equivalent conversion from complex network to time series is particularly important.With the application of classical multidimensional scaling algorithm, one of the multidimensional scaling algorithms, complex networks can be mapped to time series. This paper focuses on the solution of the Rossler&& system differential equations with specific parameters, we get the initial time series by intercepting the axis component of the solutions obtained, then this group of time series is converted to a complex network, and then CMDS algorithm will be applied to map this complex network obtained back to time series. Among this cycle, time series- complex networks- time series, we concentrate on the latter part of this cycle in which the matrix associated with the distance matrix of the complex network may have an effect on the conversion result.As is known, the Laplace matrix of a complex network is Semi-definite, we put forward a new algorithm called Laplace method here. With the knowledge that scale-free networks in the usual sense can be seen as networks obtained by connecting a number of star-typed networks whose nodes follows a power law distribution. In this paper, we discuss the result that a single star network converted to time series, a plurality of random star-star chain network converted to time series, and finally the BA scale-free networks converted to time series, all of which are realized by the Laplace methods.Besides, complex networks can be mapped to time series equivalently.Starting from the complexity of the different dynamical system, Selections of chaotic systems here include Rossler&& system, Ikeda system and the Lorenz system. We also consider sub-sequences of different lengths time series generated from the same dynamical system, Convert them into different sizes of complex networks that have the same origin, and further transform them back to time series, exploring multiscale entropy final time series. The purpose is to confirmthat complex networks with the same origin can be converted into time series with the same complexity.