Sequential motif profile of natural visibility graphs

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.

6 figures captioned

References in corpus (2)

• From time series to complex networks: the visibility graph
• Degree distribution of the visibility graphs mapped from fractional Brownian motions and multifractal random walks

Cited by in corpus (8)

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• Time Series Analysis via Network Science: Concepts and Algorithms
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• Tetradic motif profiles of horizontal visibility graphs
• Analytic degree distributions of horizontal visibility graphs mapped from unrelated random series and multifractal binomial measures
• Triadic time series motifs
• Time series classification based on triadic time series motifs
• Universal visibility patterns of unimodal maps