From time series to complex networks: The visibility graph

Author(s): Lacasa, Lucas; Luque, Bartolo; Ballesteros, Fernando; et al.

Source: PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA  Volume: 105   Issue: 13   Pages: 4972-4975   DOI: 10.1073/pnas.0709247105   Published: APR 1 2008

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 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.