Complex networks from time series: Capturing dynamics

There are now several algorithms with which one can generate a complex network representation of a time series. The basic motivation of these methods is that by performing such a transformation one can then apply a range of techniques from complex network science to the analysis and quantification of features of the time series. We will review our favorites among these techniques and then focus on what the current techniques do not do well - capture deterministic dynamical information directly. We will propose an alternative technique, the ordinal partition network transform, to do precisely this. By constructing networks from connectivity patterns among ordinal partitions of the time series we provide a parameter-free approach to study the dynamical evolution of the system directly. We show that the ordinal networks generated in this way from experimental time series data have statistical properties which provide a useful (and novel) characterisation of the underlying system.