2017/10/09 by Zhu, Yong, Chen, Xiaosong
#FOS: Physical sciences #Statistical Mechanics (cond-mat.stat-mech)
paper · doi:10.48550/arxiv.1710.02959
The k-core percolation is a fundamental structural transition in complex networks. Through the analysis of the size jump behaviors of k-core in the evolution process of networks, we confirm that k-core percolation is continuous phase transition when k=1,2 while it is a hybrid first-order-second-order phase transition when k≥ 3. 2-core percolation belongs to different universality class from that of 1-core (giant component) percolation. The discontinuity of k-core percolation with k≥ 3 can be concluded from largest size jump of k-core which will not disappear in the thermodynamic limit while its continuous characteristic is reflected by second largest size jump which converges to zero in power law as N→ ∞. Furthermore, along with the previously known exponent β=0.5, we obtain a set of exponents which are independent of k when k≥ 3 and also different from those critical exponents of 1-core and 2-core percolation.