Link rewiring with local information--induced hybrid percolation transitions

TL;DR

This paper demonstrates that local link rewiring based on cluster size information can induce hybrid percolation transitions with unique critical behavior on tree networks.

Contribution

It introduces a novel mechanism of link rewiring using local information that results in hybrid percolation transitions, expanding understanding of network phase changes.

Findings

Hybrid transitions occur with local link rewiring on Bethe lattices.

Steady states exhibit nontrivial critical exponents.

Phenomenon observed on non-hierarchical Bethe lattices.

Abstract

When a link is occupied to restrict the growth of large clusters using the size information of a finite number of finite clusters, so-called local information, an abrupt but continuous transition is exhibited. We report here that a hybrid transition can occur if each node rewires its links to restrict the growth of large clusters using local information continuously up to a finite number of rewirings. For example, on a branch of a Bethe lattice with coordination number $4$, each node rewires its outgoing links to its descendants several times in ascending order of cluster size to reach a steady state. Then a hybrid transition with nontrivial critical exponents occurs as a function of the link fraction at the steady state. We observe this phenomenon even on a Bethe lattice without hierarchy, supporting that such a phenomenon may occur on diverse tree networks with finite degrees.