# Higher-order interactions shape collective dynamics differently in hypergraphs and simplicial complexes

arXiv: https://arxiv.org/abs/2203.03060 · HTML: https://mlsanity.com/paper/2203.03060/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 Mar 2022.

## Built on by (most cited first, 12 of 12)

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- [SphUnc: Hyperspherical Uncertainty Decomposition and Causal Identification via Information Geometry](https://mlsanity.com/paper/2603.01168/) (2026)
- [XFlow: Benchmarking Flow Behaviors over Graphs](https://mlsanity.com/paper/2308.03819/) (2023)
- [Exploring higher-order neural network node interactions with total correlation](https://mlsanity.com/paper/2402.04440/) (2024)
- [Is Noise Conditioning Necessary? A Unified Theory of Unconditional Graph Diffusion Models](https://mlsanity.com/paper/2505.22935/) (2025)
- [DCHO: A Decomposition-Composition Framework for Predicting Higher-Order Brain Connectivity to Enhance Diverse Downstream Applications](https://mlsanity.com/paper/2509.09696/) (2025)
- [Learning Multi-Order Block Structure in Higher-Order Networks](https://mlsanity.com/paper/2511.21350/) (2025)
- [Unlocking the Invisible Urban Traffic Dynamics under Extreme Weather: A New Physics-Constrained Hamiltonian Learning Algorithm](https://mlsanity.com/paper/2512.03744/) (2025)
- [HYVINT: Intensity-Driven Hypergraph Generation with Variational Embeddings](https://mlsanity.com/paper/2605.16836/) (2026)

## Abstract (arXiv)

Higher-order networks have emerged as a powerful framework to model complex systems and their collective behavior. Going beyond pairwise interactions, they encode structured relations among arbitrary numbers of units through representations such as simplicial complexes and hypergraphs. So far, the choice between simplicial complexes and hypergraphs has often been motivated by technical convenience. Here, using synchronization as an example, we demonstrate that the effects of higher-order interactions are highly representation-dependent. In particular, higher-order interactions typically enhance synchronization in hypergraphs but have the opposite effect in simplicial complexes. We provide theoretical insight by linking the synchronizability of different hypergraph structures to (generalized) degree heterogeneity and cross-order degree correlation, which in turn influence a wide range of dynamical processes from contagion to diffusion. Our findings reveal the hidden impact of higher-order representations on collective dynamics, highlighting the importance of choosing appropriate representations when studying systems with nonpairwise interactions.