Higher-order components in hypergraphs

The 'order' of components in hypergraphs could be defined in terms of the number of common nodes between hyperedges. We found that hitherto largely unnoticed higher-order components (HOCs) exist ubiquitously in real-world hypergraphs, but their randomized counterparts have a very different HOCs profile. To understand the impact of HOCs, we propose a novel random hypergraph model, which has the analytically calculable giant HOC by introducing the concept of subgroups of nodes that act together during hypergraph formation process. Using the model and real-world hypergraphs, we confirm that the existence of giant HOC can significantly impact the higher-order contagion dynamics.