# Simplicial Closure and higher-order link prediction

arXiv: https://arxiv.org/abs/1802.06916 · HTML: https://mlsanity.com/paper/1802.06916/

## Key facts

- Cited by 93 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Feb 2018.

## Built on by (most cited first, 30 of 93)

- [Inductive Representation Learning in Temporal Networks via Causal Anonymous Walks](https://mlsanity.com/paper/2101.05974/) (2021)
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- [Learning Causal Effects on Hypergraphs](https://mlsanity.com/paper/2207.04049/) (2022)
- [Convolutional Learning on Simplicial Complexes](https://mlsanity.com/paper/2301.11163/) (2023)
- [Generating Interesting Scientific Ideas using Knowledge Graphs and LLMs: Evaluations with 100 Research Group Leaders](https://mlsanity.com/paper/2405.17044/) (2024)
- [BScNets: Block Simplicial Complex Neural Networks](https://mlsanity.com/paper/2112.06826/) (2021)
- [I'm Me, We're Us, and I'm Us: Tri-directional Contrastive Learning on Hypergraphs](https://mlsanity.com/paper/2206.04739/) (2022)
- [Bridging the Gap between Spatial and Spectral Domains: A Unified Framework for Graph Neural Networks](https://mlsanity.com/paper/2107.10234/) (2021)
- [A Unifying Generative Model for Graph Learning Algorithms: Label Propagation, Graph Convolutions, and Combinations](https://mlsanity.com/paper/2101.07730/) (2021)
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- [HypeBoy: Generative Self-Supervised Representation Learning on Hypergraphs](https://mlsanity.com/paper/2404.00638/) (2024)
- [Higher-order Graph Convolutional Network with Flower-Petals Laplacians on Simplicial Complexes](https://mlsanity.com/paper/2309.12971/) (2023)
- [HGWaveNet: A Hyperbolic Graph Neural Network for Temporal Link Prediction](https://mlsanity.com/paper/2304.07302/) (2023)
- [Classification of Edge-dependent Labels of Nodes in Hypergraphs](https://mlsanity.com/paper/2306.03032/) (2023)
- [Learning over Families of Sets -- Hypergraph Representation Learning for Higher Order Tasks](https://mlsanity.com/paper/2101.07773/) (2021)
- [Neural Predicting Higher-order Patterns in Temporal Networks](https://mlsanity.com/paper/2106.06039/) (2021)
- [Inference of hyperedges and overlapping communities in hypergraphs](https://mlsanity.com/paper/2204.05646/) (2022)
- [AHP: Learning to Negative Sample for Hyperedge Prediction](https://mlsanity.com/paper/2204.06353/) (2022)
- [A Comprehensive Review of Community Detection in Graphs](https://mlsanity.com/paper/2309.11798/) (2023)
- [MANTRA: The Manifold Triangulations Assemblage](https://mlsanity.com/paper/2410.02392/) (2024)
- [A nonlinear diffusion method for semi-supervised learning on hypergraphs](https://mlsanity.com/paper/2103.14867/) (2021)
- [Neural Graph Databases](https://mlsanity.com/paper/2209.09732/) (2022)
- [DYMOND: DYnamic MOtif-NoDes Network Generative Model](https://mlsanity.com/paper/2308.00770/) (2023)
- [HOT: Higher-Order Dynamic Graph Representation Learning with Efficient Transformers](https://mlsanity.com/paper/2311.18526/) (2023)
- [A Survey on Hyperlink Prediction](https://mlsanity.com/paper/2207.02911/) (2022)
- [Hypergraph Artificial Benchmark for Community Detection (h-ABCD)](https://mlsanity.com/paper/2210.15009/) (2022)
- [Quantifying Spatial Homogeneity of Urban Road Networks via Graph Neural Networks](https://mlsanity.com/paper/2101.00307/) (2021)
- [SUREL+: Moving from Walks to Sets for Scalable Subgraph-based Graph Representation Learning](https://mlsanity.com/paper/2303.03379/) (2023)

## Abstract (arXiv)

Networks provide a powerful formalism for modeling complex systems by using a model of pairwise interactions. But much of the structure within these systems involves interactions that take place among more than two nodes at once; for example, communication within a group rather than person-to person, collaboration among a team rather than a pair of coauthors, or biological interaction between a set of molecules rather than just two. Such higher-order interactions are ubiquitous, but their empirical study has received limited attention, and little is known about possible organizational principles of such structures. Here we study the temporal evolution of 19 datasets with explicit accounting for higher-order interactions. We show that there is a rich variety of structure in our datasets but datasets from the same system types have consistent patterns of higher-order structure. Furthermore, we find that tie strength and edge density are competing positive indicators of higher-order organization, and these trends are consistent across interactions involving differing numbers of nodes. To systematically further the study of theories for such higher-order structures, we propose higher-order link prediction as a benchmark problem to assess models and algorithms that predict higher-order structure. We find a fundamental differences from traditional pairwise link prediction, with a greater role for local rather than long-range information in predicting the appearance of new interactions.