## 1 Introduction  
As an important infrastructure for urban transport, the urban rail network effectively retrieves the pressure on ground transport and promotes environmental and economic sustainability due to its energy-saving, high-capacity, and non-polluting characteristics [1]. Currently, the scale of rail transport construction in China's major cities is expanding. According to the Ministry of Transportation and Communications, as of 31 December 2023, a total of 55 cities in mainland China had opened 306 urban rail transit operation lines, and the operation mileage exceeded 10,000 km, reaching 10,165.7 km [2]. Among them, 33 cities had three or more lines in operation, accounting for 60 percent of the total number of cities that had opened urban rail transit operations. This indicates that China's rail transport has entered the era of the interconnected and networked operation of stations and lines [3]. In the context of networked operation, urban rail transit is a complex system with complex lines, high equipment accuracy requirements, and a high frequency of train departures, which inevitably leads to frequent disturbances in daily operations [4]. In recent years, there has been a focus on urban rail disturbance incidents [5; 6; 7]. Disturbanceevent risk factors have been categorized as human factors [8], facility and equipment factors [9], and environmental factors [10], according to the cause of the incident. It can be seen that the failure of any subsystem or component of this complex system can lead to serious consequences in terms of train delays, stoppages, and even network paralysis [11]. Train failure, signaling failure, platform door failure, and power system failure are the four most common types of operational emergencies in daily operations, accounting for 95% of all operational emergencies [12]. Among these, signaling system failures had the highest frequency of occurrence among all disturbance events in urban rail transit, accounting for 37% of the total number of disturbances, and they are the main cause of such events [13]. In addition to the high frequency of the signaling system's own failures, human causes, mechanical failures, and environmental factors can also lead to the occurrence of signaling failures, resulting in a high frequency of signaling failures. According to New York Metro data, out of 125 morning rush hours in the first half of 2021, 104 (or 80%) of the New York Metro experienced train delays due to signaling problems [14]. According to Beijing Metro data, in the five years from 2014 to 2018, the Beijing Metro accumulated 405 primary failures of various types. All of these failures caused delays ranging from a few minutes to a few hours or even led to more serious consequences. Among these, 198 signaling failures occurred, which accounted for nearly half of them [15]. It can be seen that the frequent occurrence of signaling system failures seriously affects the safe and stable operation of urban rail transit, greatly impacting urban residents' travel. Therefore, if the critical nodes in the urban rail transit network can be found and protected in advance under the disturbance scenarios of signal system failure, it not only enhances the technical safety of the rail transit network but also helps to guarantee the network operation safety and improve the service quality. This paper intends to propose a node importance assessment method under the signaling system failure scenario and apply it to the actual case of the Nanjing Metro to identify the critical stations. Furthermore, the proposed method provides a framework for assessing the significance of nodes in practical applications across various metro networks, including those in New York, London, Beijing, Shanghai, and other extensive rail systems.