# Hyper-cores promote localization and efficient seeding in higher-order processes

arXiv: https://arxiv.org/abs/2301.04235 · HTML: https://mlsanity.com/paper/2301.04235/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Jan 2023.

## Built on by (most cited first, 2 of 2)

- [Critical Nodes Identification in Complex Networks: A Survey](https://mlsanity.com/paper/2507.06164/) (2025)
- [Learning Multi-Order Block Structure in Higher-Order Networks](https://mlsanity.com/paper/2511.21350/) (2025)

## Abstract (arXiv)

Going beyond networks, to include higher-order interactions of arbitrary sizes, is a major step to better describe complex systems. In the resulting hypergraph representation, tools to identify structures and central nodes are scarce. We consider the decomposition of a hypergraph in hyper-cores, subsets of nodes connected by at least a certain number of hyperedges of at least a certain size. We show that this provides a fingerprint for data described by hypergraphs and suggests a novel notion of centrality, the hyper-coreness. We assess the role of hyper-cores and nodes with large hyper-coreness in higher-order dynamical processes: such nodes have large spreading power and spreading processes are localized in central hyper-cores. Additionally, in the emergence of social conventions very few committed individuals with high hyper-coreness can rapidly overturn a majority convention. Our work opens multiple research avenues, from comparing empirical data to model validation and study of temporally varying hypergraphs.