State Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, Zhong-Guan-Cun East Road 55, Beijing 100190, China.
Nat Commun. 2013;4:2412. doi: 10.1038/ncomms3412.
Percolation theory concerns the emergence of connected clusters that percolate through a networked system. Previous studies ignored the effect that a node outside the percolating cluster may actively induce its inside neighbours to exit the percolating cluster. Here we study this inducing effect on the classical site percolation and K-core percolation, showing that the inducing effect always causes a discontinuous percolation transition. We precisely predict the percolation threshold and core size for uncorrelated random networks with arbitrary degree distributions. For low-dimensional lattices the percolation threshold fluctuates considerably over realizations, yet we can still predict the core size once the percolation occurs. The core sizes of real-world networks can also be well predicted using degree distribution as the only input. Our work therefore provides a theoretical framework for quantitatively understanding discontinuous breakdown phenomena in various complex systems.
渗流理论关注的是通过网络系统渗透的连通簇的出现。以前的研究忽略了一个位于渗流簇外的节点可能会主动诱导其内部邻居离开渗流簇的影响。在这里，我们研究了经典的点渗流和 K 核渗流中的这种诱导效应，结果表明诱导效应总是导致不连续的渗流转变。我们精确地预测了具有任意度分布的无关联随机网络的渗流阈值和核大小。对于低维晶格，在实现过程中渗流阈值会发生很大的波动，但一旦发生渗流，我们仍然可以预测核大小。使用度分布作为唯一输入，我们还可以很好地预测真实网络的核大小。因此，我们的工作为定量理解各种复杂系统中不连续的破坏现象提供了一个理论框架。
