J. H. Qian, D. D. Han, Y. G. Ma
This letter studies the critical point as well as the discontinuity of a class of explosive site percolation in Erd\"os and R\'enyi (ER) random network. The class of the percolation is implemented by introducing a \textit{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 -0.5 and -1. 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 to the network robustness.
View original:
http://arxiv.org/abs/1203.0299
No comments:
Post a Comment