From time series to complex networks: the visibility graph

TL;DR

This paper introduces the visibility graph, a fast method to transform time series into graphs, revealing properties like periodicity, randomness, and fractality through network analysis.

Contribution

The paper presents the visibility algorithm, a novel and efficient way to convert time series into complex networks, linking series properties to network structures.

Findings

Periodic series become regular graphs

Random series convert into random graphs

Fractal series produce scale-free networks

Abstract

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.