Complex network analysis of time series

Revealing complicated behaviors from time series constitutes a fundamental problem of continuing interest and it has attracted a great deal of attention from a wide variety of fields on account of its significant importance. The past decade has witnessed a rapid development of complex network studies, which allow to characterize many types of systems in nature and technology that contain a large number of components interacting with each other in a complicated manner. Recently, the complex network theory has been incorporated into the analysis of time series and fruitful achievements have been obtained. Complex network analysis of time series opens up new venues to address interdisciplinary challenges in climate dynamics, multiphase flow, brain functions, ECG dynamics, economics and traffic systems.  Characterizing dynamical processes in a time-dependent complex system from observed time series of just one or more variables is a fundamental problem of significant importance in many fields ranging from physics and chemistry to economy and social science. Different time series analysis methods have been developed to fulfill this challenging task, e.g., chaos analysis , fractal analysis [2,3], recurrence plot [4], complexity measure , multiscale entropy [6], and time-frequency representation . Time series analysis has been broadly adopted in scientific research and engineering applications. Many theoretical developments for time series analysis have significantly contributed to the understanding of complex systems. However, when system complexity increases, it becomes difficult to describe the dynamical behavior from time series and traditional time series analysis methods have difficulty in coping with the specific burdens of this increased complexity. During the last decade, a new multidisciplinary methodology using complex network has emerged for characterizing complex systems [8–26]. Charting the interactions among system components, abstracted as nodes and edges, has allowed us to represent a complex system as a complex network and then assess the system in terms of network theory. Recently, several novel methodologies have been proposed to map a univariate/multivariate time series into a complex network. These methods have been applied to address interdisciplinary challenges and have already proven great potential for characterizing important properties of complex dynamical systems. The literature on complex network analysis of time series is growing at a very fast rate due to its wide applications in a large variety of research fields. Complex network analysis of univariate time series. – We start from a time series xt, t = 1, 2, 3, . . . , N where N is the length of the measured record. Zhang and Small [27] were the first to construct a complex network from a pseudoperiodic time series. They divided a pseudoperiodic time series into disjoint cycles according to the local minimum (or maximum), and then constructed a network by regarding each cycle as a node and determining the connection between nodes in terms of phase space distance between the corresponding cycles. Xu and Small [28] developed an intriguing method for inferring complex network from xt and indicated that