Link rewiring with local information--induced hybrid percolation transitions

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.