Percolation of interdependent networks with intersimilarity
Percolation of interdependent networks with intersimilarity
复制标题
具有相似性的相互依存网络的渗透。
DOI：
10.1103/physreve.88.052805
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发表时间：
2013-11-07
影响因子：
2.4
通讯作者：
Havlin, Shlomo
中科院分区：
文献类型：
--
作者：
Hu, Yanqing;Zhou, Dong;Havlin, Shlomo
真实的数据表明，相互依赖的网络通常涉及相互相似性。互相似性意味着一对相互依赖的节点在两个网络中都有邻居，这些邻居也是相互依赖的[Parshani et al. Lett. 92，68002（2010）]。例如，全球港口网络和全球机场网络是相互类似的，因为在这两个网络中存在许多对通过直飞航班和直航航线连接的节点（相邻城市）。同一城市的两个网络中的节点被认为是相互依赖的。如果一个网络中的两个相邻节点依赖于另一个网络中的相邻节点，我们称这些链路为公共链路。系统中公共链接的比例是相互相似性的度量。Parshani等人先前的模拟结果表明，互相似性对减少级联故障有相当大的影响;然而，目前缺乏对级联过程的这种影响的理论理解。在这里，我们映射的级联过程中的相互相似性的渗透网络组成的组件的共同的链接和非共同的链接。这就把相似系统的渗流问题转化为一系列子网络上的正则渗流问题，从而可以解析求解。我们将我们的分析应用于以下情况：公共链接网络是平均度为K的Erdens-Rényi（ER）网络，并且两个非公共链接网络也是ER网络。我们证明了对于一对完全耦合的ER网络，对于任何K≥0，虽然级联随K的增加而减少，但相变仍然是不连续的。我们的分析可以推广到任何类型的相互依赖的随机网络系统。
Real data show that interdependent networks usually involve intersimilarity. Intersimilarity means that a pair of interdependent nodes have neighbors in both networks that are also interdependent [Parshani et al. Europhys. Lett. 92, 68002 (2010)]. For example, the coupled worldwide port network and the global airport network are intersimilar since many pairs of linked nodes (neighboring cities), by direct flights and direct shipping lines, exist in both networks. Nodes in both networks in the same city are regarded as interdependent. If two neighboring nodes in one network depend on neighboring nodes in the other network, we call these links common links. The fraction of common links in the system is a measure of intersimilarity. Previous simulation results of Parshani et al. suggest that intersimilarity has considerable effects on reducing the cascading failures; however, a theoretical understanding of this effect on the cascading process is currently missing. Here we map the cascading process with intersimilarity to a percolation of networks composed of components of common links and noncommon links. This transforms the percolation of intersimilar system to a regular percolation on a series of subnetworks, which can be solved analytically. We apply our analysis to the case where the network of common links is an Erdős-Rényi (ER) network with the average degree K, and the two networks of noncommon links are also ER networks. We show for a fully coupled pair of ER networks, that for any K≥0, although the cascade is reduced with increasing K, the phase transition is still discontinuous. Our analysis can be generalized to any kind of interdependent random network systems.