Analytic degree distributions of horizontal visibility graphs mapped from unrelated random series and multifractal binomial measures
arXiv:1902.03435 · doi:10.1209/0295-5075/119/48008
Abstract
Complex network is not only a powerful tool for the analysis of complex system, but also a promising way to analyze time series. The algorithm of horizontal visibility graph (HVG) maps time series into graphs, whose degree distributions are numerically and analytically investigated for certain time series. We derive the degree distributions of HVGs through an iterative construction process of HVGs. The degree distributions of the HVG and the directed HVG for random series are derived to be exponential, which confirms the analytical results from other methods. We also obtained the analytical expressions of degree distributions of HVGs and in-degree and out-degree distributions of directed HVGs transformed from multifractal binomial measures, which agree excellently with numerical simulations.
7 pages, 4 figures
References in corpus (5)
- From time series to complex networks: the visibility graph
- Complex Network Approach for Recurrence Analysis of Time Series
- Historical Review of Recurrence Plots
- Degree distribution of the visibility graphs mapped from fractional Brownian motions and multifractal random walks
- Multiplex visibility graphs to investigate recurrent neural networks dynamics