Percolation properties of growing networks under an Achlioptas process

Abstract

We study the percolation transition in growing networks under an Achlioptas process (AP). At each time step, a node is added in the network and, with probability δ, a link is formed between two nodes chosen by an AP. We find that there occurs the percolation transition with varying δ and the critical point δc = 0.5149(1) is determined from the power-law behavior of the order parameter and the crossing of the fourth-order cumulant at the critical point, also confirmed by the movement of the peak positions of the second largest cluster size to the δc. Using the finite-size scaling analysis, we get and , which implies β ≈ 1/2 and . The Fisher exponent τ = 2.24(1) for the cluster size distribution is obtained and shown to satisfy the hyperscaling relation.