# Networks beyond pairwise interactions: structure and dynamics

arXiv: https://arxiv.org/abs/2006.01764 · HTML: https://mlsanity.com/paper/2006.01764/

## Key facts

- Cited by 130 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 2 Jun 2020.

## Built on by (most cited first, 30 of 130)

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- [Architectures of Topological Deep Learning: A Survey of Message-Passing Topological Neural Networks](https://mlsanity.com/paper/2304.10031/) (2023)
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- [High-Order Pooling for Graph Neural Networks with Tensor Decomposition](https://mlsanity.com/paper/2205.11691/) (2022)
- [Heterogeneous manifolds for curvature-aware graph embedding](https://mlsanity.com/paper/2202.01185/) (2022)
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- [Bridging the Gap between Spatial and Spectral Domains: A Unified Framework for Graph Neural Networks](https://mlsanity.com/paper/2107.10234/) (2021)
- [Higher-order Graph Convolutional Network with Flower-Petals Laplacians on Simplicial Complexes](https://mlsanity.com/paper/2309.12971/) (2023)
- [Combinatorial Complexes: Bridging the Gap Between Cell Complexes and Hypergraphs](https://mlsanity.com/paper/2312.09504/) (2023)
- [A Survey on Large-Population Systems and Scalable Multi-Agent Reinforcement Learning](https://mlsanity.com/paper/2209.03859/) (2022)
- [Curvature-based Clustering on Graphs](https://mlsanity.com/paper/2307.10155/) (2023)
- [Inference of hyperedges and overlapping communities in hypergraphs](https://mlsanity.com/paper/2204.05646/) (2022)
- [Signal processing on simplicial complexes](https://mlsanity.com/paper/2106.07471/) (2021)
- [Copresheaf Topological Neural Networks: A Generalized Deep Learning Framework](https://mlsanity.com/paper/2505.21251/) (2025)
- [A nonlinear diffusion method for semi-supervised learning on hypergraphs](https://mlsanity.com/paper/2103.14867/) (2021)
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- [Attending to Topological Spaces: The Cellular Transformer](https://mlsanity.com/paper/2405.14094/) (2024)
- [HOT: Higher-Order Dynamic Graph Representation Learning with Efficient Transformers](https://mlsanity.com/paper/2311.18526/) (2023)
- [Learning High-Order Relationships of Brain Regions](https://mlsanity.com/paper/2312.02203/) (2023)
- [AI-enhanced Collective Intelligence](https://mlsanity.com/paper/2403.10433/) (2024)
- [Hypergraph Artificial Benchmark for Community Detection (h-ABCD)](https://mlsanity.com/paper/2210.15009/) (2022)
- [Dirac signal processing of higher-order topological signals](https://mlsanity.com/paper/2301.10137/) (2023)
- [Recommender systems based on graph embedding techniques: A comprehensive review](https://mlsanity.com/paper/2109.09587/) (2021)
- [Learning Harmonic Molecular Representations on Riemannian Manifold](https://mlsanity.com/paper/2303.15520/) (2023)
- [HOG-Diff: Higher-Order Guided Diffusion for Graph Generation](https://mlsanity.com/paper/2502.04308/) (2025)

## Abstract (arXiv)

The complexity of many biological, social and technological systems stems from the richness of the interactions among their units. Over the past decades, a great variety of complex systems has been successfully described as networks whose interacting pairs of nodes are connected by links. Yet, in face-to-face human communication, chemical reactions and ecological systems, interactions can occur in groups of three or more nodes and cannot be simply described just in terms of simple dyads. Until recently, little attention has been devoted to the higher-order architecture of real complex systems. However, a mounting body of evidence is showing that taking the higher-order structure of these systems into account can greatly enhance our modeling capacities and help us to understand and predict their emerging dynamical behaviors. Here, we present a complete overview of the emerging field of networks beyond pairwise interactions. We first discuss the methods to represent higher-order interactions and give a unified presentation of the different frameworks used to describe higher-order systems, highlighting the links between the existing concepts and representations. We review the measures designed to characterize the structure of these systems and the models proposed in the literature to generate synthetic structures, such as random and growing simplicial complexes, bipartite graphs and hypergraphs. We introduce and discuss the rapidly growing research on higher-order dynamical systems and on dynamical topology. We focus on novel emergent phenomena characterizing landmark dynamical processes, such as diffusion, spreading, synchronization and games, when extended beyond pairwise interactions. We elucidate the relations between higher-order topology and dynamical properties, and conclude with a summary of empirical applications, providing an outlook on current modeling and conceptual frontiers.