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 $2<\lambda <3$, 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 $t_c^{+}$.

arXiv comment9 pages, 9 figures, 2 tables

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Cited by in corpus (3)

• Unified framework for hybrid percolation transitions based on microscopic dynamics
• Discontinuous percolation via suppression of neighboring clusters in a network
• Discontinuous emergence of a giant cluster in assortative scale-free networks