Percolation properties of growing networks under an Achlioptas process
1 BK21 Physics Research Division and Department of Physics, Sungkyunkwan University - Suwon 440-746, Korea
2 Department of Applied Physics, Hanyang University - Ansan 426-791, Korea
Received: 23 May 2013
Accepted: 8 July 2013
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.
PACS: 64.60.ah – Percolation / 05.70.Jk – Critical point phenomena / 89.75.Da – Systems obeying scaling laws
© EPLA, 2013