A hybrid percolation transition at a finite transition point in scale-free networks.

Abstract

Percolation transition (PT) means the formation of a macroscopic-scale large cluster, which exhibits a continuous transition. However, when the growth of large clusters is globally suppressed, the type of PT is changed to a discontinuous transition for random networks. A question arises as to whether the type of PT is also changed for scale-free (SF) network, because the existence of hubs incites the formation of a giant cluster. Here, we apply a global suppression rule to the static model for SF networks and investigate properties of the PT. We find that even for SF networks with the degree exponent 2<λ<3, a hybrid PT occurs at a finite transition point tc, which we can control by the suppression strength. The order parameter jumps at tc - and exhibits a critical behavior at tc +.