From time series to complex networks: The visibility graph

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 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.Brownian motion ͉ complex systems ͉ fractals

Complex network approach to fractional time series

“…For low α's, the HV graphs are highly assortative, thus, the hubs (nodes with highest degree) have better visibility on each other, which is called hub attraction. The presence of hub attraction is due to the presence of more fluctuations in the original time series 25 , which is a consistent result, here. For anti-persistent fGn, we find again a nearly constant value for r. …”

“…More recently, a graphtheoretical approach in time series analysis has been developed, and the network-based theories have been applied in many disciplines such as biology, sociology, physics, climatology, and neurosciences [24][25][26][27][28][29][30][31] . In this approach, a time series is mapped into a (complex) graph, and the characteristics of the time series are believed to be inherited in the resulting network, which can be analyzed from a complex network perspective.…”

“…In this approach, a time series is mapped into a (complex) graph, and the characteristics of the time series are believed to be inherited in the resulting network, which can be analyzed from a complex network perspective. One of the most studied of these maps has been proposed by Lacasa et al in 2008. They introduced an algorithm 25 , called Visibility Graph (VG), which maps a time series into a graph based on the ability of the data points to see each other and it is defined as follows: Let x i be a time series of size N (i = 1, 2, ...N).…”

A comparison of two methods for modeling large-scale data from time series as complex networks

“…Wu et al (2008) 11 and Gao and Jin (2009) 12 choose a threshold of x% of the root-mean-square (rms) value of a time series in a distance method. Lacasa et al (2008) 13 In this paper, we contrast the differences between the methods based on distance and linear correlation. We find that these two connection methods transform the same time series into different network graphs.…”

Comment on “Network analysis of human heartbeat dynamics” [Appl. Phys. Lett. 96, 073703 (2010)]

“…In a recent paper, 1 Zhi-Gang Shao constructed the associated networks of time series of human heartbeat interval based on the visibility algorithm, 2 and analyzed the statistical properties of associated networks of human heartbeat dynamics. With the filtered data of five healthy subjects and five patients with congestive heart failure ͑CHF͒ in Ref.…”