Multiple discontinuous percolation transitions on scale-free networks

Abstract

Percolation transitions in networks, describing the formation of a macroscopic component, are typically considered to be robust continuous transitions in random percolation. Yet, a class of models with various rules of connecting edges were recently devised which can lead to discontinuous transitions at percolation threshold. Here we study the Bohman–Frieze–Wormald process on scale-free networks constructed via a modified configuration model. We show via numerical simulation that multiple discontinuous transitions appear in the thermodynamic limit for the degree distribution exponent λ ∈ [2, λc) with λc ∈ (2.3, 2.4). For λ ∈ (λc, 5] this model undergoes a unique discontinuous transition in the thermodynamic limit, but for any finite system a second discontinuous transition occasionally appears at some point above percolation threshold due to the aggregation of two existing giant components. For all values of the exponent λ ∈ [2, 5] we observe a pronounced right-hump in the evolution of component size distribution providing further evidence that the percolation transition is discontinuous at percolation threshold.