  In order to extract correlation information inherited in stochastic time
series, the visibility graph algorithm has been recently proposed, by which a
time series can be mapped onto a complex network. We demonstrate that the
visibility algorithm is not an appropriate one to study the correlation aspects
of a time series. We then employ the horizontal visibility algorithm, as a much
simpler one, to map fractional processes onto complex networks. The degree
distributions are shown to have parabolic exponential forms with Hurst
dependent fitting parameter. Further, we take into account other topological
properties such as maximum eigenvalue of the adjacency matrix and the degree
assortativity, and show that such topological quantities can also be used to
predict the Hurst exponent, with an exception for anti-persistent fractional
Gaussian noises. To solve this problem, we take into account the Spearman
correlation coefficient between nodes' degrees and their corresponding data
values in the original time series.

Data Analysis, Statistics and Probability;Physics and Society