Wang Hui, Li Ming, Deng Lin, Wang Bing-Hong
School of Computer and Information/Hefei University of Technology, Hefei, Anhui Province, 230009, P.R. China; Department of Modern Physics/University of Science and Technology of China, Hefei, Anhui Province, 230026, P.R. China; Information Construction and Development Center/Hefei University of Technology, Hefei, Anhui Province, 230009, P.R. China; Center of Information Support and Assurance Technology, Anhui University, Hefei, Anhui Province, 230601, P.R. China.
Department of Modern Physics/University of Science and Technology of China, Hefei, Anhui Province, 230026, P.R. China.
PLoS One. 2015 May 15;10(5):e0126674. doi: 10.1371/journal.pone.0126674. eCollection 2015.
Recently, the dependence group has been proposed to study the robustness of networks with interdependent nodes. A dependence group means that a failed node in the group can lead to the failures of the whole group. Considering the situation of real networks that one failed node may not always break the functionality of a dependence group, we study a cascading failure model that a dependence group fails only when more than a fraction β of nodes of the group fail. We find that the network becomes more robust with the increasing of the parameter β. However, the type of percolation transition is always first order unless the model reduces to the classical network percolation model, which is independent of the degree distribution of the network. Furthermore, we find that a larger dependence group size does not always make the networks more fragile. We also present exact solutions to the size of the giant component and the critical point, which are in agreement with the simulations well.
最近，提出了依赖组来研究具有相互依赖节点的网络的鲁棒性。一个依赖组意味着组中的一个故障节点可能导致整个组的故障。考虑到实际网络中一个故障节点不一定总是破坏依赖组的功能的情况，我们研究了一种级联故障模型，即只有当组中超过β比例的节点发生故障时，依赖组才会失效。我们发现，随着参数β的增加，网络变得更加鲁棒。然而，除非该模型简化为经典网络渗流模型，否则渗流转变的类型总是一阶的，这与网络的度分布无关。此外，我们发现较大的依赖组规模并不总是使网络更脆弱。我们还给出了巨分量大小和临界点的精确解，它们与模拟结果吻合得很好。
