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The physics of higher-order interactions in complex systems

arXiv 2110.06023 ↗First posted 12 Oct 2021physics.soc-ph cond-mat.dis-nn cs.SIcited by 63

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Abstract (arXiv)

Complex networks have become the main paradigm for modelling the dynamics of interacting systems. However, networks are intrinsically limited to describing pairwise interactions, whereas real-world systems are often characterized by higher-order interactions involving groups of three or more units. Higher-order structures, such as hypergraphs and simplicial complexes, are therefore a better tool to map the real organization of many social, biological and man-made systems. Here, we highlight recent evidence of collective behaviours induced by higher-order interactions, and we outline three key challenges for the physics of higher-order systems.

Key facts. Cited by 63 papers in the map (data through 7 Oct 2026). First posted on arXiv 12 Oct 2021.

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 2; 2022: 9; 2023: 17; 2024: 13; 2025: 15; 2026: 7.

63 papers.

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  1. 2023Architectures of Topological Deep Learning: A Survey of Message-Passing Topological Neural Networkscited by 43
  2. 2022Predicting the Future of AI with AI: High-quality link prediction in an exponentially growing knowledge networkcited by 34
  3. 2024TopoBench: A Framework for Benchmarking Topological Deep Learningcited by 24
  4. 2024A Survey on Hypergraph Neural Networks: An In-Depth and Step-By-Step Guidecited by 22
  5. 2024Forecasting high-impact research topics via machine learning on evolving knowledge graphscited by 21
  6. 2023Higher-order Graph Convolutional Network with Flower-Petals Laplacians on Simplicial Complexescited by 15
  7. 2022Inference of hyperedges and overlapping communities in hypergraphscited by 13
  8. 2022A Survey on Large-Population Systems and Scalable Multi-Agent Reinforcement Learningcited by 12
  9. 2024Attending to Topological Spaces: The Cellular Transformercited by 11
  10. 2023Learning High-Order Relationships of Brain Regionscited by 10
  11. 2023Dirac signal processing of higher-order topological signalscited by 9
  12. 2022Unifying Pairwise Interactions in Complex Dynamicscited by 8
38 more
  1. 2023Structure and inference in hypergraphs with node attributescited by 7
  2. 2023Topo-MLP : A Simplicial Network Without Message Passingcited by 7
  3. 2025Inferring Higher-Order Couplings with Neural Networkscited by 7
  4. 2023CAT-Walk: Inductive Hypergraph Learning via Set Walkscited by 6
  5. 2023Multi-Scale Simulation of Complex Systems: A Perspective of Integrating Knowledge and Datacited by 5
  6. 2024Integrating Physics and Topology in Neural Networks for Learning Rigid Body Dynamicscited by 5
  7. 2025HOPSE: Scalable Higher-Order Positional and Structural Encoder for Combinatorial Representationscited by 5
  8. 2022Nonbacktracking spectral clustering of nonuniform hypergraphscited by 4
  9. 2024Demystifying Higher-Order Graph Neural Networkscited by 4
  10. 2024Learning Interpretable Network Dynamics via Universal Neural Symbolic Regressioncited by 4
  11. 2024Hypergraph Attacks via Injecting Homogeneous Nodes into Elite Hyperedgescited by 4
  12. 2022Deep Ensembles for Graphs with Higher-order Dependenciescited by 3
  13. 2023Kernel-based Joint Independence Tests for Multivariate Stationary and Non-stationary Time Seriescited by 3
  14. 2023Interaction Measures, Partition Lattices and Kernel Tests for High-Order Interactionscited by 3
  15. 2024Explosive neural networks via higher-order interactions in curved statistical manifoldscited by 3
  16. 2024ICML Topological Deep Learning Challenge 2024: Beyond the Graph Domaincited by 3
  17. 2022All the World's a (Hyper)Graph: A Data Dramacited by 2
  18. 2023Zoo Guide to Network Embeddingcited by 2
  19. 2023Degree Heterogeneity in Higher-Order Networks: Inference in the Hypergraph boldsymbolβ-Modelcited by 2
  20. 2023Influential Simplices Mining via Simplicial Convolutional Networkcited by 2
  21. 2023Physics-tailored machine learning reveals unexpected physics in dusty plasmascited by 2
  22. 2024Assessing high-order effects in feature importance via predictability decompositioncited by 2
  23. 2022Linking Theories and Methods in Cognitive Sciences via Joint Embedding of the Scientific Literature: The Example of Cognitive Controlcited by 1
  24. 2024Higher order definition of causality by optimally conditioned transfer entropycited by 1
  25. 2024Dirac-Equation Signal Processing: Physics Boosts Topological Machine Learningcited by 1
  26. 2025Deep Learning Meets Process-Based Models: A Hybrid Approach to Agricultural Challengescited by 1
  27. 2025Higher-order Structure Boosts Link Prediction on Temporal Graphscited by 1
  28. 2025Permutation-Free High-Order Interaction Testscited by 1
  29. 2025On the role of non-linear latent features in bipartite generative neural networkscited by 1
  30. 2025A Survey on Agentic Service Ecosystems: Measurement, Analysis, and Optimizationcited by 1
  31. 2026Attention-based graph neural networks: a surveycited by 1
  32. 2026Learning Higher-Order Structure from Incomplete Spatiotemporal Data: Multi-Scale Hypergraph Laplacians with Neural Refinementcited by 1
  33. 2021Inference of time-ordered multibody interactionscited by 0
  34. 2021Data-Driven Interaction Analysis of Line Failure Cascading in Power Grid Networkscited by 0
  35. 2022Temporal Link Prediction via Adjusted Sigmoid Function and 2-Simplex Sructurecited by 0
  36. 2023Towards hypergraph cognitive networks as feature-rich models of knowledgecited by 0
  37. 2023XFlow: Benchmarking Flow Behaviors over Graphscited by 0
  38. 2023Topological Graph Signal Compressioncited by 0

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