Filippo Radicchi

We study scale-free networks constructed via a cooperative Achlioptas growth process. Links between nodes are introduced 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 nonvanishing percolation threshold already for lambda > lambda(c) similar to 2: 2. More interestingly, the transition is continuous when lambda <= 3 but becomes discontinuous when lambda > 3. This may have important consequences for both the structure of networks and for the dynamics of processes taking place on them.