# Node and Edge Nonlinear Eigenvector Centrality for Hypergraphs

arXiv: https://arxiv.org/abs/2101.06215 · HTML: https://mlsanity.com/paper/2101.06215/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Jan 2021.

## Built on by (most cited first, 8 of 8)

- [You are AllSet: A Multiset Function Framework for Hypergraph Neural Networks](https://mlsanity.com/paper/2106.13264/) (2021)
- [Classification of Edge-dependent Labels of Nodes in Hypergraphs](https://mlsanity.com/paper/2306.03032/) (2023)
- [Inference of hyperedges and overlapping communities in hypergraphs](https://mlsanity.com/paper/2204.05646/) (2022)
- [A nonlinear diffusion method for semi-supervised learning on hypergraphs](https://mlsanity.com/paper/2103.14867/) (2021)
- [Graph machine learning for flight delay prediction due to holding manouver](https://mlsanity.com/paper/2502.04233/) (2025)
- [A flexible PageRank-based graph embedding framework closely related to spectral eigenvector embeddings](https://mlsanity.com/paper/2207.11321/) (2022)
- [Community and hyperedge inference in multiple hypergraphs](https://mlsanity.com/paper/2505.04967/) (2025)
- [Identifying Group Anchors in Real-World Group Interactions Under Label Scarcity](https://mlsanity.com/paper/2509.20762/) (2025)

## Abstract (arXiv)

Network scientists have shown that there is great value in studying pairwise interactions between components in a system. From a linear algebra point of view, this involves defining and evaluating functions of the associated adjacency matrix. Recent work indicates that there are further benefits from accounting directly for higher order interactions, notably through a hypergraph representation where an edge may involve multiple nodes. Building on these ideas, we motivate, define and analyze a class of spectral centrality measures for identifying important nodes and hyperedges in hypergraphs, generalizing existing network science concepts. By exploiting the latest developments in nonlinear Perron-Frobenius theory, we show how the resulting constrained nonlinear eigenvalue problems have unique solutions that can be computed efficiently via a nonlinear power method iteration. We illustrate the measures on realistic data sets.