Mapping time series to complex networks: the visibility algorithm

The visibility algorithm is a method that map time series into socalled visibility graphs according to a specific geometric criterion. In so doing, methods from complex network theory can be fruitfully used for time series analysis purposes. Concretely, the topological analysis of the resulting graphs provide nontrivial information of the time series, and, consequently, of the dynamical process that generated such series. After addressing some specific examples on how the algorithm maps series of different garment to their associated visibility graphs, I will address the task of (a) discriminate chaotic series from random uncorrelated series and (b) quantify the Hurst exponent of fractal series by means of the visibility algorithm. I will finally point out some further applications and open problems.