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A recently proposed methodology called the Horizontal Visibility Graph (HVG)[Luque {\it et al.}, Phys. Rev. E., 80, 046103 (2009)] that constitutes ageometrical simplification of the well known Visibility Graph algorithm [Lacasa{\it et al.\/}, Proc. Natl. Sci. U.S.A. 105, 4972 (2008)], has been used tostudy the distinction between deterministic and stochastic components in timeseries [L. Lacasa and R. Toral, Phys. Rev. E., 82, 036120 (2010)].Specifically, the authors propose that the node degree distribution of theseprocesses follows an exponential functional of the form $P(\kappa)\sim\exp(-\lambda~\kappa)$, in which $\kappa$ is the node degree and $\lambda$ is apositive parameter able to distinguish between deterministic (chaotic) andstochastic (uncorrelated and correlated) dynamics. In this work, we investigatethe characteristics of the node degree distributions constructed by using HVG,for time series corresponding to $28$ chaotic maps and $3$ different stochasticprocesses. We thoroughly study the methodology proposed by Lacasa and Toralfinding several cases for which their hypothesis is not valid. We propose amethodology that uses the HVG together with Information Theory quantifiers. Anextensive and careful analysis of the node degree distributions obtained byapplying HVG allow us to conclude that the Fisher-Shannon information plane isa remarkable tool able to graphically represent the different nature,deterministic or stochastic, of the systems under study.

Distinguishing noise from chaos: objective versus subjective criteria using Horizontal Visibility Graph