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arXiv · 1605.02645

Sequential motif profile of natural visibility graphs

Jacopo Iacovacci·Lucas Lacasa
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Abstract

The concept of sequential visibility graph motifs -subgraphs appearing with characteristic frequencies in the visibility graphs associated to time series- has been advanced recently along with a theoretical framework to compute analytically the motif profiles associated to Horizontal Visibility Graphs (HVGs). Here we develop a theory to compute the profile of sequential visibility graph motifs in the context of Natural Visibility Graphs (VGs). This theory gives exact results for deterministic aperiodic processes with a smooth invariant density or stochastic processes that fulfil the Markov property and have a continuous marginal distribution. The framework also allows for a linear time numerical estimation in the case of empirical time series. A comparison between the HVG and the VG case (including evaluation of their robustness for short series polluted with measurement noise) is also presented.

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Jacopo Iacovacci, Lucas Lacasa. 2016-05-09. Sequential motif profile of natural visibility graphs. https://doi.org/10.1103/physreve.94.052309

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