Criticality and continuity of explosive site percolation in random networks
1 Shanghai Institute of Applied Physics, Chinese Academy of Sciences - Shanghai 201800, China
2 School of Information Science and Technology, East China Normal University - Shanghai 200241, China
Received: 23 April 2012
Accepted: 7 November 2012
This letter studies the critical point as well as the discontinuity of a class of explosive site percolation in Erdös and Rényi (ER) random network. The class of the percolation is implemented by introducing a best-of-m rule. Two major results are found: i) For any specific m, the critical percolation point scales with the average degree of the network while its exponent associated with m is bounded by −1 and ∼ − 0.5. ii) Discontinuous percolation could occur on sparse networks if and only if m approaches infinite. These results not only generalize some conclusions of ordinary percolation but also provide new insights into the network robustness.
PACS: 89.75.Hc – Networks and genealogical trees / 89.75.Da – Systems obeying scaling laws
© EPLA, 2012