Encapsulation Structure and Dynamics in Hypergraphs

TL;DR

This paper investigates the structure of real-world hypergraphs, focusing on hyperedge encapsulation, and shows how these structural patterns influence diffusive dynamics, particularly spreading processes.

Contribution

It introduces measures for hyperedge encapsulation in hypergraphs and analyzes their impact on diffusion dynamics, linking structure to function.

Findings

Encapsulation patterns vary across real-world hypergraphs.

Non-random encapsulation accelerates spreading processes.

Measures quantify hyperedge relations and compatibility with simplicial complexes.

Abstract

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.