Local suppression by link rewiring reveals discontinuous percolation transitions

Abstract

When a governor occupies links one by one to globally suppress the formation of large clusters, a macroscopic cluster emerges discontinuously. We report here a mechanism by which a macroscopic cluster emerges discontinuously when each node rewires its links to locally suppress the formation of large clusters as links are occupied. In this manner, each node may compete with its neighbors to suppress the growth of its cluster, but the formation of a macroscopic cluster is suppressed cooperatively, and this results in discontinuous percolation transitions. This result implies that each entity actively participating in suppressing macroscopic phenomena, such as an epidemic or forest fire, could potentially lead to a rapid outbreak.