  In this work we present a simple and fast computational method, the
visibility algorithm, that converts a time series into a graph. The constructed
graph inherits several properties of the series in its structure. Thereby,
periodic series convert into regular graphs, and random series do so into
random graphs. Moreover, fractal series convert into scale-free networks,
enhancing the fact that power law degree distributions are related to
fractality, something highly discussed recently. Some remarkable examples and
analytical tools are outlined in order to test the method's reliability. Many
different measures, recently developed in the complex network theory, could by
means of this new approach characterize time series from a new point of view.
