# Dynamics on higher-order networks: A review

arXiv: https://arxiv.org/abs/2203.06601 · HTML: https://mlsanity.com/paper/2203.06601/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Mar 2022.

## Built on by (most cited first, 11 of 11)

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- [Learning the effective order of a hypergraph dynamical system](https://mlsanity.com/paper/2306.01813/) (2023)
- [Higher-Order Causal Structure Learning with Additive Models](https://mlsanity.com/paper/2511.03831/) (2025)
- [Fedivertex: a Graph Dataset based on Decentralized Social Networks for Trustworthy Machine Learning](https://mlsanity.com/paper/2505.20882/) (2025)
- [Prismal view of ethics](https://mlsanity.com/paper/2205.13370/) (2022)
- [XFlow: Benchmarking Flow Behaviors over Graphs](https://mlsanity.com/paper/2308.03819/) (2023)
- [Leveraging Personalized PageRank and Higher-Order Topological Structures for Heterophily Mitigation in Graph Neural Networks](https://mlsanity.com/paper/2507.16347/) (2025)
- [Learning Multi-Order Block Structure in Higher-Order Networks](https://mlsanity.com/paper/2511.21350/) (2025)
- [Average shortest-path length in word-adjacency networks: Chinese versus English](https://mlsanity.com/paper/2601.06361/) (2026)

## Abstract (arXiv)

Network science has evolved into an indispensable platform for studying complex systems. But recent research has identified limits of classical networks, where links connect pairs of nodes, to comprehensively describe group interactions. Higher-order networks, where a link can connect more than two nodes, have therefore emerged as a new frontier in network science. Since group interactions are common in social, biological, and technological systems, higher-order networks have recently led to important new discoveries across many fields of research. We here review these works, focusing in particular on the novel aspects of the dynamics that emerges on higher-order networks. We cover a variety of dynamical processes that have thus far been studied, including different synchronization phenomena, contagion processes, the evolution of cooperation, and consensus formation. We also outline open challenges and promising directions for future research.