# Neighborhood-based Hypergraph Core Decomposition

arXiv: https://arxiv.org/abs/2301.06426 · HTML: https://mlsanity.com/paper/2301.06426/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 Jan 2023.

## Built on by (most cited first, 1 of 1)

- [Identifying Group Anchors in Real-World Group Interactions Under Label Scarcity](https://mlsanity.com/paper/2509.20762/) (2025)

## Abstract (arXiv)

We propose neighborhood-based core decomposition: a novel way of decomposing hypergraphs into hierarchical neighborhood-cohesive subhypergraphs. Alternative approaches to decomposing hypergraphs, e.g., reduction to clique or bipartite graphs, are not meaningful in certain applications, the later also results in inefficient decomposition; while existing degree-based hypergraph decomposition does not distinguish nodes with different neighborhood sizes. Our case studies show that the proposed decomposition is more effective than degree and clique graph-based decompositions in disease intervention and in extracting provably approximate and application-wise meaningful densest subhypergraphs. We propose three algorithms: Peel, its efficient variant E-Peel, and a novel local algorithm: Local-core with parallel implementation. Our most efficient parallel algorithm Local-core(P) decomposes hypergraph with 27M nodes and 17M hyperedges in-memory within 91 seconds by adopting various optimizations. Finally, we develop a new hypergraph-core model, the (neighborhood, degree)-core by considering both neighborhood and degree constraints, design its decomposition algorithm Local-core+Peel, and demonstrate its superiority in spreading diffusion.