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 the 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 $δ_c=0.5149(1)$ is determined from the power-law behavior of 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 $δ_c$. Using the finite-size scaling analysis, we get $β/\barν=0.20(1)$ and $1/\barν=0.40(1)$, which implies $β\approx 1/2$ and $\barν \approx 5/2$. The Fisher exponent $τ= 2.24(1)$ for the cluster size distribution is obtained and shown to satisfy the hyperscaling relation.

4 pages, 5 figures, 1 table, journal submitted