Explosive percolation in scale-free networks

TL;DR

This paper investigates a new growth process for scale-free networks that results in a percolation transition with unique properties, including a non-zero threshold and a change from continuous to discontinuous phase transition depending on the degree exponent.

Contribution

It introduces a cooperative Achlioptas growth process for scale-free networks, revealing novel percolation transition behaviors not seen in standard models.

Findings

Percolation threshold is non-zero for lambda > 2.2.

Transition is continuous for lambda <= 3.

Transition becomes discontinuous for lambda > 3.

Abstract

We study scale-free networks constructed via a cooperative Achlioptas growth process. Links between nodes are introduced in the network in order to produce a scale-free graph with given exponent lambda for the degree distribution, but the choice of each new link depends on the mass of the clusters that this link will merge. Networks constructed via this biased procedure show a percolation transition which strongly differs from the one observed in standard percolation, where links are introduced just randomly. The different growth process leads to a phase transition with a non-vanishing percolation threshold already for lambda > lambda_c ~ 2.2. More interestingly, the transition is continuous when lambda <= 3 but becomes discontinuous when lambda > 3. This may have important consequences both for the structure of networks and for the dynamics of processes taking place on them.