Higher-Order Components Dictate Higher-Order Contagion Dynamics in Hypergraphs

TL;DR

This paper demonstrates that the presence of a giant higher-order component in hypergraphs is essential for the global spread of contagion, significantly impacting collective behavior in complex systems.

Contribution

It reveals the critical role of the giant higher-order component in enabling higher-order contagion to spread globally on hypergraphs, a novel insight into hypergraph dynamics.

Findings

Giant HOC alters contagion outbreak patterns

Giant HOC is necessary for global contagion invasion

Synthetic hypergraphs confirm the role of HOC in contagion dynamics

Abstract

The presence of the giant component is a necessary condition for the emergence of collective behavior in complex networked systems. Unlike networks, hypergraphs have an important native feature that components of hypergraphs might be of higher order, which could be defined in terms of the number of common nodes shared between hyperedges. Although the extensive higher-order component (HOC) could be witnessed ubiquitously in real-world hypergraphs, the role of the giant HOC in collective behavior on hypergraphs has yet to be elucidated. In this Letter, we demonstrate that the presence of the giant HOC fundamentally alters the outbreak patterns of higher-order contagion dynamics on real-world hypergraphs. Most crucially, the giant HOC is required for the higher-order contagion to invade globally from a single seed. We confirm it by using synthetic random hypergraphs containing adjustable and analytically calculable giant HOC.