Random formation of Borromean networks in the presence of Hopf-linked connections

Establish whether Borromean networks can randomly form when Hopf-linked (regularly linked) networks are present in the same system of randomly linked rings, clarifying the conditions for coexistence or mutual exclusion of these topologies.

Background

In highly entangled systems where many Hopf links exist, a ring linked with all nearby neighbors may not be able to participate in Borromean triplets, raising the question of whether Borromean connectivity can emerge alongside extensive pairwise linking.

The paper introduces a simplified rectangle model to probe whether Borromean hypergraphs can arise within or alongside Hopf-linked percolating clusters.