From time series to complex networks: The visibility graph

By Lucas Lacasa, B. Luque, Fernando J. Ballesteros, Jordi Luque, J. C. Nuño. Proceedings of the National Academy of Sciences of the United States of America, 2008

1,655 citations recorded by the source corpus.

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.

Subfields: Condensed Matter Physics, Economics and Econometrics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/a0c1483e0e34fb9bc1baf929ce892f111e329fa6

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Citations in the corpus

A novel hybrid method of forecasting crude oil prices using complex network science and artificial intelligence algorithms (2018, methodology): “Complex network theory has been recently applied to the analysis of time series and has yielded high-quality results [36 – 39].”
Wavelet Multiresolution Complex Network for Analyzing Multivariate Nonlinear Time Series (2017, background): “…and many successful applications have been achieved in different research fields [Wang et al., 2016; Zhang et al., 2006; 2008; Xu et al., 2008; Lacasa et al., 2008; Marwan et al., 2009; Majhi et al., 2016; Wang et al., 2015; Xiang et al., 2012; Marwan & Kurths, 2015; Peng et al., 2013; Wang…”
Complex network approach for recurrence analysis of time series (2009, background): “od [5]). Other approaches for the study of time series by a complex network analysis suggested using linear correlations [34] or another certain condition on the time series amplitudes (“visibility”) [35]. In this letter, we demonstrate that the recurrence matrix (analogously to [31]) can be conside”
Analysis and Classification of Sleep Stages Based on Difference Visibility Graphs From a Single-Channel EEG Signal (2014, methodology): “[18] have been employed to analyze EEG signals [7], [19], [20].”
A Survey of Methods for Time Series Change Point Detection (2016, neutral): “This graph can be defined based on a minimum spanning tree [26], minimum distance pairing [52], nearest neighbor graph [26,52], or visibility graph [40,66].”
Superfamily phenomena and motifs of networks induced from time series (2008, methodology): “R a bridge between time series analysis and complex networks has emerged (1, 2).”
Irreversibility and complex network behavior of stream flow fluctuations (2016, methodology): “[28] as a special case of the visibility 10 algorithm [20,21] to map stream flow time series into graphs.”
The role of fluctuating modes of autocorrelation in crude oil prices (2014, background): “proposed the visibility graph algorithm, which can map all types of time series into networks [11].”
Exact results of the limited penetrable horizontal visibility graph associated to random time series and its application (2017, methodology): “The second one is the visibility graph (VG) method, which was ﬁrst proposed by Lacasa et al. [9–10].”