Extending transfer operator methods and clustering beyond graphs

Determine whether and how transfer operator frameworks and their associated clustering methods can be extended to hypergraphs, simplicial complexes, and graphons.

Background

The article develops connections between transfer operators and graph-based clustering, including for directed and time-evolving graphs. However, many modern networked systems are naturally modeled as higher-order structures such as hypergraphs and simplicial complexes or via graphon limits.

A generalization of transfer operator theory and clustering methodologies to these settings would broaden applicability but remains unresolved.