1301.2895 (Hai-Jun Zhou et al.)

(K, K')-Protected Core Percolation    [PDF]

Hai-Jun Zhou, Jin-Hua Zhao, Yang-Yu Liu

We present an analytical theory for the (K, K')-protected core percolation problem. Each initially protected vertex transits to the susceptible state if it has less than K protected neighbors or if one of its susceptible neighbors has less than K' protected neighbors. The theory predicts (K, K')-protected core percolation to be a discontinuous transition for any type of uncorrelated networks and any K, K'> 1. We check these predictions by extensive computer simulations for the representative cases of K'=K. For random networks both the transition point and the (K, K)-protected core size are predicted precisely by our theory. For low-dimensional lattices the transition point fluctuates considerably, but our theory still predicts precisely the (K, K)-protected core size once the transition occurs. The theory is also applied successfully to real-world complex networks.

View original: http://arxiv.org/abs/1301.2895