Analytic Degree Distributions and Optimal Sliding-Window Lengths of Sliding Horizontal Visibility Graphs Mapped from Multifractal Binomial Measures

Over the recent years, the study of Sliding Visibility Graph (SVG) algorithm has attracted great interests. The SVG algorithm is an effective method for quickly mapping time series to complex networks. In this paper, we propose the Sliding Horizontal Visibility Graph (SHVG) algorithm, a geometrically simpler and analytically solvable version of SVG algorithm . After introducing some properties of this new algorithm, we present exact results on the degree distributions and the optimal sliding-window lengths of SHVG mapped from multifractal binomial measures, which agree excellently with numerical simulations. SHVG algorithm and the original Horizontal Visibility Graph ( HVG) algorithm are further used to study the meteorological time series in Xi’an. The result shows that the SHVG algorithm has a greater performance in computational efficiency