title: Multifractal analysis of visibility graph-based Ito-related connectivity time series.
abstract: In this study, we investigate multifractal properties of connectivity time series resulting from the visibility graph applied to normally distributed time series generated by the Ito equations with multiplicative power-law noise. We show that multifractality of the connectivity time series (i.e., the series of numbers of links outgoing any node) increases with the exponent of the power-law noise. The multifractality of the connectivity time series could be due to the width of connectivity degree distribution that can be related to the exit time of the associated Ito time series. Furthermore, the connectivity time series are characterized by persistence, although the original Ito time series are random; this is due to the procedure of visibility graph that, connecting the values of the time series, generates persistence but destroys most of the nonlinear correlations. Moreover, the visibility graph is sensitive for detecting wide "depressions" in input time series.
authors.affiliation: Institute of Geophysics, Polish Academy of Sciences, 01-452 Warsaw, Ks. Janusza 64, Poland.
authors.forename: Zbigniew
authors.initials: Z
authors.lastname: Czechowski
authors.affiliation: ARPAB, 85100 Potenza, Italy.
authors.forename: Michele
authors.initials: M
authors.lastname: Lovallo
authors.affiliation: National Research Council, Institute of Methodologies for Environmental Analysis, C.da S. Loja, 85050 Tito (PZ), Italy.
authors.forename: Luciano
authors.initials: L
authors.lastname: Telesca