Abstract: In order to study the influence of multi-layer network modeling method and structural characteristics, multi-layer network node importance calculation and cascade failure process on the dynamic change of vulnerability, this paper first uses the multi-layer network theory to construct a two-layer transport network topology model and analyze its topological characteristics. Then, a multi-layer network node importance calculation method is proposed, and a load-capacity cascade failure model considering node capacity, node status and node importance is designed. Finally, the factors and changes affecting network vulnerability are simulated and analyzed. The research shows that the China-Europe sea-rail double-layer transportation network conforms to the scale-free characteristics of the complex network. Additionally, the inter-layer mismatch coupling connection, the node capacity coefficient, the different types of nodes and the load distribution method have a great influence on the network vulnerability, and the rationality of the calculation method of the node importance of the multi-layer network is verified. The conclusion shows that the important nodes should be protected first in the event of an emergency, and a certain amount of load redundancy space should be reserved when designing the station to improve the load bearing capacity after the node fails.

Key words: complex networks, multi-layer network, node importance, cascading failure, network vulnerability

摘要： 为研究多层网络建模方法及结构特性、多层网络节点重要度计算与级联失效过程各因素对脆弱性动态变化的影响，利用多层网络理论构建双层运输网络拓扑模型并分析其拓扑特性，提出一种多层网络节点重要度计算方法，并设计考虑节点容量、节点状态、节点重要度的负载-容量级联失效模型，仿真分析影响网络脆弱性的因素与变化规律。研究表明，中欧海铁双层运输网络符合复杂网络的无标度特性，网络层间异配耦合连接，节点容量系数、不同类型节点及负载分配方式对网络脆弱性影响较大，并验证了多层网络节点重要度计算方法的合理性。结论显示，发生突发事件时要优先保护重要节点，设计车站时要预留一定负载冗余空间，以提升节点失效后的负载承受能力。

关键词: 复杂网络, 多层网络, 节点重要性, 级联失效, 网络脆弱性