# Encapsulation Structure and Dynamics in Hypergraphs

arXiv: https://arxiv.org/abs/2307.04613 · HTML: https://mlsanity.com/paper/2307.04613/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Jul 2023.

## Built on by (most cited first, 5 of 5)

- [Broad Spectrum Structure Discovery in Large-Scale Higher-Order Networks](https://mlsanity.com/paper/2505.21748/) (2025)
- [HyperS2V: A Framework for Structural Representation of Nodes in Hyper Networks](https://mlsanity.com/paper/2311.04149/) (2023)
- [Edge Probability Graph Models Beyond Edge Independency: Concepts, Analyses, and Algorithms](https://mlsanity.com/paper/2405.16726/) (2024)
- [MARIOH: Multiplicity-Aware Hypergraph Reconstruction](https://mlsanity.com/paper/2504.00522/) (2025)
- [Identifying Group Anchors in Real-World Group Interactions Under Label Scarcity](https://mlsanity.com/paper/2509.20762/) (2025)

## Abstract (arXiv)

Hypergraphs have emerged as a powerful modeling framework to represent systems with multiway interactions, that is systems where interactions may involve an arbitrary number of agents. Here we explore the properties of real-world hypergraphs, focusing on the encapsulation of their hyperedges, which is the extent that smaller hyperedges are subsets of larger hyperedges. Building on the concept of line graphs, our measures quantify the relations existing between hyperedges of different sizes and, as a byproduct, the compatibility of the data with a simplicial complex representation -- whose encapsulation would be maximum. We then turn to the impact of the observed structural patterns on diffusive dynamics, focusing on a variant of threshold models, called encapsulation dynamics, and demonstrate that non-random patterns can accelerate the spreading in the system.