Wavelet-based multiscale similarity measure for complex networks

  • Ankit AgarwalEmail author
  • Rathinasamy Maheswaran
  • Norbert Marwan
  • Levke Caesar
  • Jürgen Kurths
Regular Article


In recent years, complex network analysis facilitated the identification of universal and unexpected patterns in complex climate systems. However, the analysis and representation of a multiscale complex relationship that exists in the global climate system are limited. A logical first step in addressing this issue is to construct multiple networks over different timescales. Therefore, we propose to apply the wavelet multiscale correlation (WMC) similarity measure, which is a combination of two state-of-the-art methods, viz. wavelet and Pearson’s correlation, for investigating multiscale processes through complex networks. Firstly we decompose the data over different timescales using the wavelet approach and subsequently construct a corresponding network by Pearson’s correlation. The proposed approach is illustrated and tested on two synthetics and one real-world example. The first synthetic case study shows the efficacy of the proposed approach to unravel scale-specific connections, which are often undiscovered at a single scale. The second synthetic case study illustrates that by dividing and constructing a separate network for each time window we can detect significant changes in the signal structure. The real-world example investigates the behavior of the global sea surface temperature (SST) network at different timescales. Intriguingly, we notice that spatial dependent structure in SST evolves temporally. Overall, the proposed measure has an immense potential to provide essential insights on understanding and extending complex multivariate process studies at multiple scales.


Statistical and Nonlinear Physics 


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Copyright information

© EDP Sciences, SIF, Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Potsdam Institute for Climate Impact Research (PIK), Member of the Leibniz AssociationTelegrafenbergGermany
  2. 2.Institute of Earth and Environmental Science, University of PotsdamPotsdamGermany
  3. 3.GFZ German Research Centre for GeosciencesTelegrafenbergGermany
  4. 4.Civil Engineering Department, MVGR College of EngineeringVizianagaramIndia
  5. 5.Institute of Physics and Astronomy, University of PotsdamPotsdamGermany
  6. 6.Institute of Physics, Humboldt Universität zu BerlinBerlinGermany

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