Higher-Order Interactions

Overview

• F. Battiston, C. Bick, M. Lucas, A. P. Millán, P. S. Skardal, and Y. Zhang, Collective dynamics on higher-order networks, arXiv:2510.05253

Dynamics on hypergraphs

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)

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, Sci. Adv. 10, ado8049 (2024)
• P. S. Skardal, F. Battiston, M. Lucas, M. S. Mizuhara, G. Petri, and Y. Zhang, Mixed higher-order coupling stabilizes new states, arXiv:2510.09387

Hypergraphs from dynamics

Can we infer causal 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, Nat. Commun. 16, 2691 (2025)

Temporal networks

How to do stability analysis of cluster synchronization states on generalized networks?

• 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)

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

• Y. Zhang and S. H. Strogatz, Designing temporal networks that synchronize under resource constraints, Nat. Commun. 12, 3273 (2021)
• Y. Zhang† and S. P. Cornelius, Tempological Control of Network Dynamics, arXiv:2510.10926