Higher-Order Interactions

Hypergraphs and simplicial complexes

Do higher-order interactions promote synchronization? Should we use hypergraphs or simplicial complexes when modeling systems with higher-order interactions?

  • Y. Zhang*, M. Lucas*, and F. Battiston, Higher-order interactions shape collective dynamics differently in hypergraphs and simplicial complexes, Nat. Commun. 14, 1605 (2023)

How to do stability analysis of cluster synchronization states on hypergraphs?

  • Y. Zhang, V. Latora, and A. E. Motter, Unified treatment of synchronization patterns in generalized networks with higher-order, multilayer, and temporal interactions, Commun. Phys. 4, 195 (2021)

Can we infer the underlying hypergraphs from time-series data in a model-free fashion? How important are higher-order interactions in the brain?

  • R. Delabays, G. De Pasquale, F. Dörfler, and Y. Zhang, Hypergraph reconstruction from dynamics, arXiv:2402.00078

Can higher-order interactions affect linear stability and basin stability differently?

  • Y. Zhang, P. S. Skardal, F. Battiston, G. Petri, and M. Lucas, Deeper but smaller: Higher-order interactions increase linear stability but shrink basins, arXiv:2309.16581

Temporal networks

Do temporal networks have a fundamental advantage over static networks? Can time-varying connections be used as a control mechanism?