Phase transitions and stability of dynamical processes on hypergraphs

Understand

Hypergraphs naturally represent higher-order interactions, which persistently appear from social interactions to neural networks and other natural systems.

• Although their importance is well recognized, a theoretical framework to describe general dynamical processes on hypergraphs is not available yet.
• In this paper, we bridge this gap and derive expressions for the stability of dynamical systems defined on an arbitrary hypergraph.
• The framework allows us to reveal that, near the fixed point, the relevant structure is the graph-projection of the hypergraph and that it is possible to identify the role of each structural order for a given process.