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

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