# Measuring Method of Node Importance of Urban Rail Network Based on H Index
## 1 Introduction
The literature [10] provides us with a method of using PageRank algorithm to sort nodes in urban network. In the literature [11] in the improved PageRank model, the data matrix is constructed according to the original idea of PageRank vector. Regardless of the topological distance between nodes, it gives the same opportunity to jump from one node to another. The improved algorithm is applied to the real urban network. The above references provide a reliable theoretical background for the study of the importance of urban rail network nodes. However, due to the correlation of passenger flow in the urban rail network, these methods cannot be directly applied. The passenger flows between stations are mutually influential, and their volatility characteristics are very similar. Considering the spatial correlation characteristics, a method based on \(h\)-index is proposed to study the node importance. In recent years, some scholars have attempted to apply \(h\)-index [12] and its variants to the study of complex networks. The literature [13] used the Hirsch index to identify influential communicators in the network and found it to be superior to the recently introduced non-backtracking centrality indicator. The literature [14] believed that identifying the influential nodes in the dynamic process was the key to understanding the structure and function of the network. By constructing an H operator, the relationship between node degree, \(h\)-index, and kernel number was explained as follows: node degree, \(h\)-index, and kernel number are the initial state, intermediate state, and steady state of the sequence. In the measurement of the key categories of software systems, the literature [15] defined the \(h\)-index based on nodes and node-based edge weights, which improved the existing research [14]. However, the influence of the combination of node degree and edge weight on the importance of the node was not considered. For this reason, literature [16] proposed the concept of neighbor weight in a software system. Considering the influence of the degree of neighbor nodes and the community of connected edges on the nodes, the variant index of \(h\)-index was defined, and good results were obtained in the identification of important classes. In summary, researchers have borrowed the \(h\)-index to study the measurement of the importance of nodes in software networks, but have not applied the \(h\)-index to the study of the importance metrics of urban traffic network nodes. This paper introduces the \(h\)-index idea into the traffic field to study the importance of nodes in the urban rail network and identify its key nodes. The index of \(h_{r}\) combines the spatial correlation of passenger flow in the urban rail network. In addition, it considers the topology, passenger volume, and passenger flow correlation of the urban rail network. The structure of this paper is as follows: Section 2 describes the basic theory of urban rail network node importance measurements. In Section 3, a calculation method of node importance in urban rail network based on \(h\)-index was proposed; In Section 4, the proposed method is validated and discussed by using passenger flow data and network topology data in a real urban rail network. Section 5 concludes the paper.