The urban rail network system plays a significant role in the urban transportation system and urban economic development. Further study of the urban rail network properties can provide additional guidance to related scholars and designers. This study explored urban rail network properties worldwide, including assessments of their static and dynamic network topologic characteristics. Statically, this study analyzed various related network topological indicators for all of these urban rail networks. We found that, with increasing network size, the average degree slightly increases while the complexity and connectivity decrease. Using the Kolmogorov–Smirnov goodness-of-fit, the scale of the degree interval of these cities is [3.5 12.2]. Approximately 90% of these cities have network efficiency values less than 0.12, and 78% of these cities have lower assortativity coefficients. Focusing on the sustainable growth of rail networks, this study tested some specific networks to further deliberate their network expansion ability, network growth, and network robustness properties. The network expansion capability of small networks is relatively poor, while that of large networks is relatively strong. A simulation of network growth suggests that the connection of nodes with the maximum path length will seriously affect the efficiency and characteristics of the network. The robustness of the network indicates that adopting the maximum nodal degree elimination strategy will affect the function of the network. The results provide essential reference information for the rational planning, structural optimization, safe operation and sustainable growth of rail transit networks.

中文翻译：

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全球城市轨道网拓扑特征与可持续发展

城市轨道网系统在城市交通系统和城市经济发展中发挥着重要作用。对城市轨道网特性的进一步研究可为相关学者和设计人员提供额外的指导。本研究探索了全球城市轨道网络的特性，包括对其静态和动态网络拓扑特征的评估。本研究静态分析了所有这些城市轨道网络的各种相关网络拓扑指标。我们发现，随着网络规模的增加，平均度数略有增加，而复杂性和连通性降低。使用 Kolmogorov-Smirnov 拟合优度，这些城市的度数区间尺度为 [3.5 12.2]。这些城市中大约 90% 的网络效率值低于 0.12，这些城市中有 78% 的分类系数较低。本研究以铁路网络的可持续发展为重点，对部分特定网络进行了测试，以进一步考察其网络扩展能力、网络增长和网络鲁棒性。小型网络的网络扩展能力相对较差，而大型网络的网络扩展能力相对较强。网络增长的模拟表明，具有最大路径长度的节点的连接将严重影响网络的效率和特性。网络的鲁棒性表明，采用最大节点度消除策略会影响网络的功能。研究结果为合理规划、结构优化、