# Hyperedge Prediction using Tensor Eigenvalue Decomposition

arXiv: https://arxiv.org/abs/2102.04986 · HTML: https://mlsanity.com/paper/2102.04986/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 38 references that are in the map.
- First posted on arXiv 6 Feb 2021.

## Builds on (most cited first, 8 of 8)

- [Simplicial Closure and higher-order link prediction](https://mlsanity.com/paper/1802.06916/) (2018)
- [Contact patterns in a high school: a comparison between data collected using wearable sensors, contact diaries and friendship surveys](https://mlsanity.com/paper/1506.03645/) (2015)
- [Generative hypergraph clustering: from blockmodels to modularity](https://mlsanity.com/paper/2101.09611/) (2021)
- [Uniform Hypergraph Partitioning: Provable Tensor Methods and Sampling Techniques](https://mlsanity.com/paper/1602.06516/) (2016)
- [Strongly Local Hypergraph Diffusions for Clustering and Semi-supervised Learning](https://mlsanity.com/paper/2011.07752/) (2020)
- [HPRA: Hyperedge Prediction using Resource Allocation](https://mlsanity.com/paper/2006.11070/) (2020)
- [Predicting Multi-actor collaborations using Hypergraphs](https://mlsanity.com/paper/1401.6404/) (2014)
- [Hypergraph Partitioning using Tensor Eigenvalue Decomposition](https://mlsanity.com/paper/2011.07683/) (2020)

## Built on by (most cited first, 3 of 3)

- [A Survey on Hyperlink Prediction](https://mlsanity.com/paper/2207.02911/) (2022)
- [AI-driven Hypergraph Network of Organic Chemistry: Network Statistics and Applications in Reaction Classification](https://mlsanity.com/paper/2208.01647/) (2022)
- [BERT4FCA: A Method for Bipartite Link Prediction using Formal Concept Analysis and BERT](https://mlsanity.com/paper/2402.08236/) (2024)

## Abstract (arXiv)

Link prediction in graphs is studied by modeling the dyadic interactions among two nodes. The relationships can be more complex than simple dyadic interactions and could require the user to model super-dyadic associations among nodes. Such interactions can be modeled using a hypergraph, which is a generalization of a graph where a hyperedge can connect more than two nodes. In this work, we consider the problem of hyperedge prediction in a k-uniform hypergraph. We utilize the tensor-based representation of hypergraphs and propose a novel interpretation of the tensor eigenvectors. This is further used to propose a hyperedge prediction algorithm. The proposed algorithm utilizes the textitFiedler eigenvector computed using tensor eigenvalue decomposition of hypergraph Laplacian. The textitFiedler eigenvector is used to evaluate the construction cost of new hyperedges, which is further utilized to determine the most probable hyperedges to be constructed. The functioning and efficacy of the proposed method are illustrated using some example hypergraphs and a few real datasets. The code for the proposed method is available on https://github.com/d-maurya/hypred_ tensorEVD