Unveiling the connectivity of complex networks using ordinal transition methods

TL;DR

This paper introduces a novel ordinal transition entropy method to analyze and distinguish the topological roles of nodes in complex networks of dynamical systems, demonstrating superior performance over existing measures.

Contribution

It proposes an ordinal transition entropy approach that effectively uncovers network structure and node roles from time series data, applicable to real-world correlated signals.

Findings

Ordinal transition entropy outperforms standard measures in network topology discrimination.

The method successfully characterizes the roles of nodes in chaotic Rössler networks.

Experimental data confirms applicability to real-world nonlinear oscillator networks.

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 R\"ossler 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.