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.
arXiv comment7 pages, 4 figures
References in corpus (25)
- Statistical mechanics of complex networks
- The structure and function of complex networks
- The structure of scientific collaboration networks
- Recurrence Plots for the Analysis of Complex Systems
- Who is the best connected scientist? A study of scientific coauthorship networks
- From time series to complex networks: the visibility graph
- Recurrence networks - A novel paradigm for nonlinear time series analysis
- Complex Network Approach for Recurrence Analysis of Time Series
- The Visibility Graph: a new method for estimating the Hurst exponent of fractional Brownian motion
- Historical Review of Recurrence Plots
- Description of stochastic and chaotic series using visibility graphs
- Temporal Graphs
- Network structure of multivariate time series
- Time series irreversibility: a visibility graph approach
- Statistical properties of visibility graph of energy dissipation rates in three-dimensional fully developed turbulence
- Degree distribution of the visibility graphs mapped from fractional Brownian motions and multifractal random walks
- From the time series to the complex networks: the parametric (dynamical) natural visibility graph
- Distinguishing noise from chaos: objective versus subjective criteria using Horizontal Visibility Graph
- Horizontal visibility graphs transformed from fractional Brownian motions: Topological properties versus Hurst index
- Sequential visibility-graph motifs
- Horizontal Visibility graphs generated by type-I intermittency
- On the degree distribution of horizontal visibility graphs associated to Markov processes and dynamical systems: diagrammatic and variational approaches
- Sequential motif profile of natural visibility graphs
- Fractal Analysis on Human Behaviors Dynamics
- Multiplex visibility graphs to investigate recurrent neural networks dynamics