Higher-order simplicial synchronization of coupled topological signals

@article{Ghorbanchian2020HigherorderSS,
  title={Higher-order simplicial synchronization of coupled topological signals},
  author={Reza Ghorbanchian and Juan G. Restrepo and Joaqu{\'i}n J. Torres and Ginestra Bianconi},
  journal={Communications Physics},
  year={2020},
  volume={4},
  pages={1-13}
}
Simplicial complexes capture the underlying network topology and geometry of complex systems ranging from the brain to social networks. Here we show that algebraic topology is a fundamental tool to capture the higher-order dynamics of simplicial complexes. In particular we consider topological signals, i.e., dynamical signals defined on simplices of different dimension, here taken to be nodes and links for simplicity. We show that coupling between signals defined on nodes and links leads to… 
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