Next Article in Journal
Mechanical Properties and Microstructure of a NiCrFeCoMn High-Entropy Alloy Deformed at High Strain Rates
Next Article in Special Issue
A Novel Belief Entropy for Measuring Uncertainty in Dempster-Shafer Evidence Theory Framework Based on Plausibility Transformation and Weighted Hartley Entropy
Previous Article in Journal
Liquid Phase Separation in High-Entropy Alloys—A Review
Previous Article in Special Issue
Cross-Sectoral Information Transfer in the Chinese Stock Market around Its Crash in 2015
Article Menu
Issue 11 (November) cover image

Export Article

Open AccessArticle
Entropy 2018, 20(11), 891;

Improving Entropy Estimates of Complex Network Topology for the Characterization of Coupling in Dynamical Systems

National Institute for Laser, Plasma and Radiation Physics, RO-077125 Magurele-Bucharest, Romania
Consorzio RFX (CNR, ENEA, INFN, Universita’ di Padova, Acciaierie Venete SpA), 35127 Padova, Italy
EUROfusion Consortium, JET, Culham Science Centre, Abingdon OX14 3DB, UK
Department of Industrial Engineering, University of Rome Tor Vergata, 00133 Rome, Italy
Author to whom correspondence should be addressed.
Received: 24 October 2018 / Revised: 13 November 2018 / Accepted: 19 November 2018 / Published: 20 November 2018
Full-Text   |   PDF [1866 KB, uploaded 20 November 2018]   |  


A new measure for the characterization of interconnected dynamical systems coupling is proposed. The method is based on the representation of time series as weighted cross-visibility networks. The weights are introduced as the metric distance between connected nodes. The structure of the networks, depending on the coupling strength, is quantified via the entropy of the weighted adjacency matrix. The method has been tested on several coupled model systems with different individual properties. The results show that the proposed measure is able to distinguish the degree of coupling of the studied dynamical systems. The original use of the geodesic distance on Gaussian manifolds as a metric distance, which is able to take into account the noise inherently superimposed on the experimental data, provides significantly better results in the calculation of the entropy, improving the reliability of the coupling estimates. The application to the interaction between the El Niño Southern Oscillation (ENSO) and the Indian Ocean Dipole and to the influence of ENSO on influenza pandemic occurrence illustrates the potential of the method for real-life problems. View Full-Text
Keywords: system coupling; cross-visibility graphs; image entropy; geodesic distance system coupling; cross-visibility graphs; image entropy; geodesic distance

Graphical abstract

This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).

Share & Cite This Article

MDPI and ACS Style

Craciunescu, T.; Murari, A.; Gelfusa, M. Improving Entropy Estimates of Complex Network Topology for the Characterization of Coupling in Dynamical Systems. Entropy 2018, 20, 891.

Show more citation formats Show less citations formats

Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Related Articles

Article Metrics

Article Access Statistics



[Return to top]
Entropy EISSN 1099-4300 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert
Back to Top