# Measuring Method of Node Importance of Urban Rail Network Based on H Index
## 1 Introduction  
Urban rail transit is the backbone of the transportation system. With the network operation of rail transit and the rapid increase of passenger flow, the operation safety risks of rail transit are increased, for instance, operational accidents can cause trains in local section stops or can even lead to severe casualties and breakdown of the entire network system. Meanwhile, many scholars have discussed the cascading failure phenomenon in urban rail network [1; 2; 3]. This shows that when some key stations fail, they will cause other stations to fail through the connection between stations, which greatly reduces the transmission efficiency of the urban rail network, and even leads to a global crash. Therefore, accurate identification of key stations is an effective way to reduce the safety risk of urban rail operation and improve the transportation efficiency. With the deepening of the research on the importance of nodes in urban rail networks, the existing research can be divided into the following three categories:  
* Evaluation method of node importance considering cascading failure. In this method, the following two steps are used to evaluate the importance of the nodes in an urban rail network: (1) remove the nodes from the network, (2) measure the decline rate of network efficiency. In the literature [1], the Shanghai metro network is taken as an example to study the vulnerability of the subway network to random failures of nodes and deliberate attacks on nodes. It is found that the attack strategy based on the number of betweenness centrality has the most devastating impact on the urban rail network, that is, nodes with a large number of betweenness centrality are more important. In the literature [2; 3], considering the distributioncharacteristics of passenger flow in the Nanjing metro network, the cascading failure mechanism of metro network stations is analyzed based on the \"capacity-load\" model, and different passenger flow distribution methods are proposed. In this way, the evaluation index of node importance is the ratio of the station capacity to the actual passenger flow. However, this method relies on the accuracy of \"load\" distribution, and passengers have autonomous path decision-making behavior, which will affect the evaluation of node importance in urban rail network. * Evaluation method of node importance based on network topology. Previous researchers have revealed valuable insights into the structure of metro infrastructure networks, including scale-free features [4], small-world properties [5], node centrality [6; 7; 8; 9]. Among them, the metrics of node centrality can be divided into two categories: (1) local centrality measure, (2) global centrality measure. The evaluation index of local centrality is degree centrality. The idea of the degree centrality method is that the more direct neighbors a node has, the more important it is. In the literature [6; 7], the topological characteristics of the Minsk metro network, Shanghai Metro network, Seoul metro network, and Boston metro network were discussed respectively, and the average degree of the network is calculated. The second kind of index tries to evaluate the importance of nodes from the perspective of global network. The representative evaluation indexes are betweenness centrality, the closeness centrality, and eigenvector centrality. Compared with the local centrality, the global centrality can obtain better results [8]. In the literature [9], the topological characteristics of the Beijing metro network were discussed, and the global topological index such as clustering coefficient, betweenness, and degree were calculated. These studies typically focused on the complex network topology of subway systems. * Evaluation method of node importance based on eigenvector index. The most relevant method for our work is the third one, which not only considers the number of adjacent nodes, but also their relative importance [8]. A typical example of this method is PageRank [10; 11].