2012/01/12 by Jingfang Fan, Maoxin Liu, Fan, Jingfang +5
Mathematics · Physics and Astronomy · #Complex Network Analysis Techniques #FOS: Physical sciences #Opinion Dynamics and Social Influence #Statistical Mechanics (cond-mat.stat-mech) #Stochastic processes and statistical mechanics
paper · pdf · doi:10.48550/arxiv.1201.2507
openalex publication_date 2012/01/12 · openalex created_date 2019/06/27 · openalex updated_date 2026/07/28
Using the finite-size scaling, we have investigated the percolation phase transitions of evolving random networks under a generalized Achlioptas process (GAP). During this GAP, the edge with minimum product of two connecting cluster sizes is taken with a probability p from two randomly chosen edges. This model becomes the Erd\H os-Rényi network at p=0.5 and the random network under the Achlioptas process at p=1. Using both the fixed point of s2/s1 and the straight line of ln s1, where s1 and s2 are the reduced sizes of the largest and the second largest cluster, we demonstrate that the phase transitions of this model are continuous for 0.5 ≤ p ≤ 1. From the slopes of ln s1 and ln (s2/s1)' at the critical point we get the critical exponents β and ν, which depend on p. Therefore the universality class of this model should be characterized by p also.