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

Sequential motif profile of natural visibility graphs