# Study on the Evolution and Resilience of Rail Transit Time Networks--Evidence from China
## 1 Introduction and Literature Review
[PERSON] first introduced the theory of resilience into the field of scientific research and defined ecosystem resilience as a property that persists within a system. Defining the basis of resilience is the idea that a system can persist robustly or be destroyed suddenly [4]. The root causes of rail network failures are mainly due to infrastructure [5] and vehicle issues [6], and various types of natural disaster events, health and safety and other emergencies have imposed stricter requirements on the operation of rail transportation networks [7; 8]. Therefore, it is important to strengthen the network risk analysis [9]. The network resilience analysis can applied to study the adverse effects of disruptions [10; 11], preparing optimal infrastructure restoration and traffic recovery plans [12], and diverse disturbance considerations are beneficial for avoiding potential hidden threats [13]. Existing research argues that resilience can integrate the resilience and recovery capacity of transportation systems in facing external shocks [14], and the formation and evolution process of resilience will help us to understand the performance change patterns of rail transportation networks under environmental or manmade disturbances. This way, managers can clarify the identification of and metrics and optimization methods for network resilience, which is beneficial to the operation and emergency management of rail transportation network systems. In an environment in which urban connectivity is increasingly diverse and the transportation network structure is more complex, there are still shortcomings in the resilience of the rail network, and the ability of the network to cope with interference and to resist attacks needs to be enhanced. Complex network theory originated in the early 18 th century, and it was initially applied to graph theory and network topology in the field of mathematics. [PERSON] et al. proposed the \"small-world\" network model, and [PERSON] proposed the \"scale-free\" net work model, which opened up new perspectives in the study of complex networks, with an increasingly wide range of applications for complex networks. The network model can be used as a powerful tool for analyzing rail transportation networks. Scholars introduced static and dynamic topology metrics based on complex networks to evaluate the performance of transportation networks in terms of connectivity [15; 16], accessibility [17], network structure characteristics, and resilience to destruction [18; 19; 20]. Regarding the study of rail transit networks, scholars have chosen quantitative analysis more often compared to qualitative analysis accounts. They eventually found that node disturbance strategies for systems are insufficient for resolving network failures, and network performance is more stable under random disturbance strategies. It is generally believed that more damaging nodes to the network are more important, and their disturbance can lead to failures much faster [21]. [PERSON] used centrality to identify this node importance [22]. Disturbance strategies can also be considered in terms of node degree values, clustering coefficients [23] and other indicators. The literature has also considered transportation system operations in network resilience studies, including methods that weigh passenger flow data with connected edges [24] or that consider different situations such as roadway capacity and passenger emergency response [25], but these studies rarely involve the dimension of rail transit time. The railroad train running time and train arrangement are relatively fixed, and the important measure for maintaining the stability of the network is the resilience and recovery ability. Therefore, a method of constructing a directional time-weighted network model with the running time between stations as the weight value is more in line with realistic needs.