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From time series to complex networks: the visibility graph. (English) Zbl 1205.05162

Summary: 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.

MSC:

05C62 Graph representations (geometric and intersection representations, etc.)
05C80 Random graphs (graph-theoretic aspects)
05C90 Applications of graph theory
37M10 Time series analysis of dynamical systems
62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
68M10 Network design and communication in computer systems
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