Discontinuous percolation transitions in growing networks

Abstract

Growing networks are ubiquitous in the real world, ranging from co-authorship socio-networks to protein interaction bio-networks. It is conventionally known that the giant cluster in such growing networks emerges continuously with infinite-order critical behavior. In this study, we show that when the growth of large clusters is suppressed with global information, the continuous percolation transition changes to a discontinuous transition with an abrupt jump of the order parameter at a delayed transition point p c. Moreover, a second-order-type critical behavior appears in a wide region of the link occupation probability before the system explodes, in which while the largest cluster has not grown to the extensive size of the system yet, the mean cluster size diverges. Far below p c, the property of the infinite-order transition still remains. Accordingly, the features of infinite-order, second-order, and first-order transitions all occur in a single framework when the infinite-order transition is suppressed. We present a simple argument to explain the underlying mechanism of these abnormal transition behaviors. Finally, we show that this result is universal by examining percolation transitions of a protein-interacting-network model.