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 delta, a link is formed between two nodes chosen by an AP. We find that there occurs the percolation transition with varying delta and the critical point delta(c) = 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 delta(c). Using the finite-size scaling analysis, we get beta/(nu) over bar = 0.20(1) and 1/(nu) over bar = 0.40(1), which implies beta approximate to 1/2 and (nu) over bar approximate to 5/2. The Fisher exponent tau = 2.24(1) for the cluster size distribution is obtained and shown to satisfy the hyperscaling relation. Copyright (C) EPLA, 2013