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 $\delta$, 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 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 $\beta /\bar{\nu }=0.20(1)$ and $1/\bar{\nu }=0.40(1)$, which implies $\beta \approx 1/2$ and $\bar{\nu }\approx 5/2$. The Fisher exponent $\tau =2.24(1)$ for the cluster size distribution is obtained and shown to satisfy the hyperscaling relation.

4 pages, 5 figures, 1 table, journal submitted

References in corpus (8)

• Critical phenomena in complex networks
• Explosive Percolation is Continuous, but with Unusual Finite Size Behavior
• Explosive percolation in scale-free networks
• Avoiding a Spanning Cluster in Percolation Models
• Entrainment transition in populations of random frequency oscillators
• Continuity of the Explosive Percolation Transition
• Suppression effect on explosive percolations
• Critical Phase of Bond Percolations on Growing Networks

Cited by in corpus (9)

• Explosive transitions in complex networks' structure and dynamics: percolation and synchronization
• Percolation on complex networks: Theory and application
• Explosive Phenomena in Complex Networks
• Explosive Percolation: Novel critical and supercritical phenomena
• Explosive Percolation: Unusual Transitions of a Simple Model
• Method for estimating critical exponents in percolation processes with low sampling
• Explosive percolation in finite dimensions
• Percolation Transitions in Growing Networks Under Achlioptas Processes: Analytic Solutions
• Structural Properties of Networks Grown via an Achlioptas Process