Revealing Network Symmetries Using Time-Series Data
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.
- 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