Evidence of Self-Organised Criticality in Time Series by the Horizontal Visibility Graph Approach

Abstract

Determination of self-organised criticality (SOC) is crucial in evaluating the dynamical behavior of a time series. Here, we apply the complex network approach to assess the SOC characteristics in synthesis and real-world data sets. To this purpose, we employ the horizontal visibility graph (HVG) method and construct the relevant networks for the observational and numerical avalanching events (e.g., earthquakes and sand-pile models), financial markets, and the solar nano-flare emission model, which showed to have long-temporal correlations via re-scaled range analysis. We compute the degree distribution, maximum eigenvalue, and average clustering coefficient of each HVG and compare them with the values obtained for random and chaotic processes. The result manifests a perceptible deviation between these parameters in random and SOC time series. We conclude that the mentioned HVG’s features can distinguish between SOC and random systems.