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Unveiling the Connectivity of Complex Networks Using Ordinal Transition Methods.

Juan A Almendral1,2, I Leyva1,2, Irene Sendiña-Nadal1,2

  • 1Complex Systems Group & Grupo Interdisciplinar de Sistemas Complejos (GISC), Universidad Rey Juan Carlos, 28933 Móstoles, Madrid, Spain.

Entropy (Basel, Switzerland)
|July 29, 2023
PubMed
Summary

We introduce a novel permutation entropy measure for analyzing complex networks. This method effectively distinguishes the topological roles of networked chaotic systems, outperforming existing complexity measures.

Keywords:
chaotic synchronizationcomplex networksordinal patternsordinal permutation entropyordinal transition network

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Area of Science:

  • Complex Systems Science
  • Network Science
  • Nonlinear Dynamics

Background:

  • Ordinal measures are useful for correlated data series analysis.
  • Understanding information flow and network structure in dynamical systems using ordinal methods is underexplored.
  • Existing methods struggle to differentiate network roles during synchronization.

Purpose of the Study:

  • To compare ordinal permutation entropy with a new permutation entropy measure based on ordinal transition matrices.
  • To assess the effectiveness of these measures in identifying the topological roles of nodes in networked chaotic systems.
  • To demonstrate the applicability of the novel method to real-world time series data.

Main Methods:

  • Calculated ordinal permutation entropy for time series data.
  • Developed and applied permutation entropy based on ordinal transition probability matrices.
  • Tested measures on networked chaotic Rössler systems.
  • Validated the method using experimental data from nonlinear oscillator networks.

Main Results:

  • The permutation entropy of the ordinal transition matrix significantly outperformed standard ordinal permutation entropy.
  • The proposed method effectively discriminated the topological roles of nodes in networked chaotic systems.
  • The method demonstrated robustness in analyzing experimental time series data.

Conclusions:

  • Permutation entropy of ordinal transition matrices offers a powerful new tool for network analysis.
  • This approach can uncover network structure from time series data, even with unknown underlying networks.
  • The method is applicable to diverse real-world systems exhibiting correlations and network structures.