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

TL;DR

This paper investigates how global suppression influences percolation transitions in scale-free networks, revealing a hybrid transition at a controllable finite point with both discontinuous and critical features.

Contribution

It introduces a global suppression rule to scale-free networks and demonstrates the emergence of a hybrid percolation transition at a finite critical point.

Findings

Hybrid percolation transition occurs in SF networks with 2<λ<3.

Transition point t_c can be controlled by suppression strength.

Order parameter shows a jump and critical behavior at t_c.

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 $2 < \lambda <3$, a hybrid PT occurs at a finite transition point $t_c$, which we can control by the suppression strength. The order parameter jumps at $t_c^-$ and exhibits a critical behavior at $t_c^+$.