Unveiling the connectivity of complex networks using ordinal transition methods

Abstract

Ordinal measures provide a valuable collection of tools for analyzing correlated data series. However, using these methods to understand the information interchange in networks of dynamical systems, and uncover the interplay between dynamics and structure during the synchronization process, remains relatively unexplored. Here, we compare the ordinal permutation entropy, a standard complexity measure in the literature, and the permutation entropy of the ordinal transition probability matrix that describes the transitions between the ordinal patterns derived from a time series. We find that the permutation entropy based on the ordinal transition matrix outperforms the rest of the tested measures in discriminating the topological role of networked chaotic Rössler systems. Since the method is based on permutation entropy measures, it can be applied to arbitrary real-world time series exhibiting correlations originating from an existing underlying unknown network structure. In particular, we show the effectiveness of our method using experimental datasets of networks of nonlinear oscillators.

9 pages, 5 figures

References in corpus (11)

• From time series to complex networks: the visibility graph
• Time lagged ordinal partition networks for capturing dynamics of continuous dynamical systems
• Synchronizability determined by coupling strengths and topology on Complex Networks
• Conditional entropy of ordinal patterns
• Hub Synchronization in Scale-Free Networks
• Characterizing stochastic time series with ordinal networks
• Time Series Analysis via Network Science: Concepts and Algorithms
• Quantifying sudden changes in dynamical systems using symbolic networks
• Ordinal methods for a characterization of evolving functional brain networks
• Statistical complexity and connectivity relationship in cultured neural networks
• Ordinal Poincaré Sections: Reconstructing the First Return Map from an Ordinal Segmentation of Time Series