依赖群对网络功能的临界作用
The critical effect of dependency groups on the function of networks
摘要：
当前的网络模型假设一种类型的链接来定义网络实体之间的关系。然而，许多真实网络只能使用两种不同类型的关系来正确描述。使节点能够作为网络协同工作的连接性链路，以及将一个网络元件的故障绑定到其他网络元件的故障的依赖性链路。在这里，我们首次提出了一个分析框架，用于研究网络的鲁棒性，包括连接和依赖性链接。我们发现，这两种类型的故障之间的协同作用导致级联故障的迭代过程，对网络的稳定性具有破坏性的影响，并完全改变了已知的假设网络的鲁棒性。我们提出了精确的分析结果，在网络行为的戏剧性变化时，引入依赖链接。对于高密度的依赖性链接，网络以一阶相变的形式分解，而对于低密度的依赖性链接，网络以二阶相变分解。此外，与仅包含连接性链接的网络相反，更广泛的度分布会导致更强大的网络，当两种类型的链接都存在时，广泛的度分布会导致更高的脆弱性。
英文摘要：
Current network models assume one type of links to define the relations between the network entities. However, many real networks can only be correctly described using two different types of relations. Connectivity links that enable the nodes to function cooperatively as a network and dependency links that bind the failure of one network element to the failure of other network elements. Here we present for the first time an analytical framework for studying the robustness of networks that include both connectivity and dependency links. We show that the synergy between the two types of failures leads to an iterative process of cascading failures that has a devastating effect on the network stability and completely alters the known assumptions regarding the robustness of networks. We present exact analytical results for the dramatic change in the network behavior when introducing dependency links. For a high density of dependency links the network disintegrates in a form of a first order phase transition while for a low density of dependency links the network disintegrates in a second order transition. Moreover, opposed to networks containing only connectivity links where a broader degree distribution results in a more robust network, when both types of links are present a broad degree distribution leads to higher vulnerability.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
