Revealing Network Symmetries Using Time-Series Data

  • Ethan T. H. A. van Woerkom
  • Joseph D. HartEmail author
  • Thomas E. Murphy
  • Rajarshi Roy
Conference paper
Part of the Understanding Complex Systems book series (UCS)


Complex dynamical networks may exhibit graph symmetries. These symmetries leave an imprint on network behaviour and statistics. This effect is first demonstrated in a small opto-electronic network. We then present the general conditions under which network statistics become invariant under the action of network symmetries. Statistical analyses can help reveal the symmetry group of a network graph without knowledge of the underlying network model. Finally, results from numerical experiments additionally demonstrate this.



This paper is a result of work performed as part of the TREND NSF REU program and the University of Maryland, College Park. JDH and RR are thankful for support from ONR Grant No. N000141612481. EvW is thankful for the aid of Olwen Enright and Timea Vitos for constructive input on the manuscript and Keshav Rakesh for his patient aid writing the proofs.


  1. 1.
    S. Pajevic, D. Plenz, Efficient network reconstruction from dynamical cascades identifies small-world topology of neuronal avalanches. PLoS Comput. Biol. 5(1), e1000271 (2009)MathSciNetCrossRefGoogle Scholar
  2. 2.
    A. Pikovsky, Reconstruction of a neural network from a time series of firing rates. Phys. Rev. E 93, 062313 (2016)MathSciNetCrossRefGoogle Scholar
  3. 3.
    J.D. Hart, K. Bansal, T.E. Murphy, R. Roy, Experimental observation of chimera and cluster states in a minimal globally coupled network. Chaos 26, 094801 (2016)MathSciNetCrossRefGoogle Scholar
  4. 4.
    A.B. Siddique, L. Pecora, J.D. Hart, F. Sorrentino, Symmetry- and input-cluster synchronization in networks. Phys. Rev. E 97, 042217 (2018)CrossRefGoogle Scholar
  5. 5.
    L.M. Pecora, F. Sorrentino, A.M. Hagerstrom, T.E. Murphy, R. Roy, Cluster synchronization and isolated desynchronization in complex networks with symmetries. Nat. Commun. 5, 4079 (2014)Google Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Ethan T. H. A. van Woerkom
    • 1
  • Joseph D. Hart
    • 2
    • 3
    Email author
  • Thomas E. Murphy
    • 2
    • 4
  • Rajarshi Roy
    • 2
    • 3
    • 5
  1. 1.School of Physics and AstronomyUniversity of EdinburghEdinburghUK
  2. 2.Institute for Research in Electronics and Applied PhysicsUniversity of MarylandCollege ParkUSA
  3. 3.Department of PhysicsUniversity of MarylandCollege ParkUSA
  4. 4.Department of Electrical and Computer EngineeringUniversity of MarylandCollege ParkUSA
  5. 5.Institute for Physical Science and TechnologyUniversity of MarylandCollege ParkUSA

Personalised recommendations