Xie Jiarong, Yuan Youyou, Fan Zhengping, Wang Jiahai, Wu Jiajing, Hu Yanqing
School of Data and Computer Science, Sun Yat-sen University, Guangzhou 510006, China.
Chaos. 2019 Aug;29(8):083111. doi: 10.1063/1.5093077.
The dependency among nodes has significant effects on the cascading failures of complex networks. Although the prevention of cascading failures on multilayered networks in which the failures of nodes in one layer affect the functioning of nodes in other layers has been widely investigated, the prevention of catastrophic cascade has rarely been addressed to single-layer networks where nodes are grouped and nodes within the same group are dependent on each other. For such networks, we find that it is already enough to prevent abrupt catastrophic collapses by randomly reinforcing a constant density of nodes. More importantly, we give the analytical solutions to the proportion of needed reinforced nodes for three typical networks, i.e., dependent Erdős-Rényi (ER), random regular (RR), and scale-free (SF) networks. Interestingly, the density of reinforced nodes is a constant 0.1756, which holds true for ER networks with group size 2 regardless of average degree, RR, and SF networks with a large average degree. Also, we find the elegant expression of the density with any group size. In addition, we find a hybrid phase transition behavior, which is present in RR and SF networks while absent in ER networks. Our findings might shed some new light on designing more resilient infrastructure networks.
节点之间的依赖性对复杂网络的级联故障有重大影响。尽管多层网络中级联故障的预防已得到广泛研究，其中一层节点的故障会影响其他层节点的功能，但对于节点分组且同一组内节点相互依赖的单层网络，灾难性级联的预防却很少被提及。对于此类网络，我们发现通过随机强化固定密度的节点就足以防止突然的灾难性崩溃。更重要的是，我们给出了三种典型网络（即相依的厄多斯 - 雷尼（ER）网络、随机正则（RR）网络和无标度（SF）网络）所需强化节点比例的解析解。有趣的是，强化节点的密度为常数0.1756，对于组大小为2的ER网络，无论平均度如何，以及平均度较大的RR网络和SF网络均成立。此外，我们还找到了任意组大小下密度的简洁表达式。另外，我们发现了一种混合相变行为，它存在于RR网络和SF网络中，而在ER网络中不存在。我们的发现可能为设计更具弹性的基础设施网络提供一些新的思路。
