融合复杂网络与攻击模拟的城市轨道交通网络抗毁性分析

王中政¹，顼玉卿^2，3*

1.河北地质大学城市地质与工程学院，河北 石家庄  050031；2.河北地质大学管理学院，河北 石家庄  050031;

3.石家庄铁道大学管理学院，河北 石家庄  050043

摘要：为系统评估城市轨道交通网络应对不确定性干扰的抵御能力，以石家庄城市轨道交通（规划）网络为研究对象，基于复杂网络理论，采用Space-L方法构建无向无权网络拓扑模型，通过计算度分布、平均路径长度、聚类系数等拓扑参数识别网络特征，设计涵盖节点与连边失效的6种攻击策略，结合网络效率和最大连通子图比例评估城市轨道交通网络在随机攻击与蓄意攻击场景下的网络抗毁性，采用模拟单节点和单连边失效的方式识别关键节点和关键连边。结果表明：通过对比石家庄轨道交通（规划）网络与随机网络的拓扑参数，计算得到小世界网络指数s=1.110 3>1.000 0，且度分布近似服从泊松分布，表明该网络具有小世界网络特性；该网络对基于节点度与节点介数的蓄意攻击较敏感，对基于连边介数的攻击表现出较强韧性；不同节点或连边失效对网络效率影响差异显著，节点和连边的静态拓扑指标（度、介数）与其失效所引起的实际网络性能下降不存在正相关关系。应通过强化关键站点与区间防护、优化网络拓扑结构、建立多模式交通应急联运体系增强石家庄城市轨道交通（规划）网络的抗毁性。

关键词：城市轨道交通；复杂网络；抗毁性；关键节点；关键连边

Resilience analysis of urban rail transit networks integrating complex networks and attack simulation

WANG Zhongzheng¹, XU Yuqing^2,3*

1. School of Urban Geology and Engineering, Hebei GEO University, Shijiazhuang 050031, China;

2. School of Management, Hebei GEO University, Shijiazhuang 050031, China;

3. School of Management, Shijiazhuang Tiedao University, Shijiazhuang 050043, China

Abstract: To systematically evaluate the ability of urban rail transit networks to withstand uncertain disruptions, this study takes the Shijiazhuang urban rail transit (planned) network as the research object. Based on complex network theory, an undirected and unweighted topology is constructed using the Space-L method. Network characteristics are identified by computing topological parameters such as degree distribution, average path length, and clustering coefficient. Six attack strategies covering node and edge failures are designed, and network resilience under random and targeted attacks is assessed using network efficiency and the proportion of the largest connected component. Critical nodes and edges are identified through sequential single-node and single-edge failure experiments. Results show that, compared with a corresponding random network, the Shijiazhuang (planned) network yields a small-world index of s=1.110 3>1.000 0, and its degree distribution approximately follows a Poisson distribution, indicating small-world properties. The network is sensitive to targeted attacks based on node degree and node betweenness, while it exhibits stronger robustness to attacks based on edge betweenness. The impacts of different node or edge failures on network efficiency vary markedly, and static topological indicators (degree, betweenness) are not in a simple positive correspondence with the actual performance degradation caused by their failures. Resilience should be enhanced by strengthening the protection of critical stations and track sections, optimizing the network topology, and establishing a multimodal emergency intermodal system.

Keywords: urban rail transit; complex network; resilience; critical node; critical edge