# Measuring Method of Node Importance of Urban Rail Network Based on H Index
## 3 Method for Calculating the Importance of Urban Rail Network Nodes Based on \(h\)-Index
### Methodology  
In the \(h\)-index defined by [PERSON], scientists publish papers in descending order of citations and then calculate index values to evaluate scientists' scientific contributions. Scientists can be considered as nodes, and the papers represent the attributes of nodes. In this study, firstly, the coefficient of the other nodes in the urban rail network to node \(i\) is calculated. Then, sort the coefficients in descending order. Finally, the \(h_{r}\) index and \(g_{r}\) index of the urban rail network nodes are calculated according to Definitions 3 and 4, thereby evaluating the importance of the urban rail station. In fact, [PERSON]'s \(h\)-index measures scientists from the perspective of the paper. The difference in this study is that the proposed index is calculated based on the level of \"scientists\" rather than the \"paper\" level. The \(h_{r}\) index and the \(g_{r}\) index obtained by such a calculation concept are more objective in evaluating the importance of the node. For example, a transfer site in a urban rail network has four neighbor nodes. Assume that node \(i\) contains only four attributes (adjacent nodes, corresponding to the scientist's \"paper\"), and other nodes have a higher correlation with the node. At the time, if the \(h\)-index of the node is calculated based on the \"paper\" level, the value of the index can be up to 4. However, if the \(h\)-index is calculated from the level of \"scientist\", the limit of the attribute value can be broken, and the value can better reflect the importance of the node.  
The process of calculating the importance degree of urban rail network nodes based on \(h\)-index is shown in Figure 2.  
Figure 2: Process of calculating the importance degree of urban rail transit network nodes based on \(h\)-index.  
The method of calculating the importance degree of urban rail network nodes based on \(h\)-index is mainly divided into the following steps:  
Input: Urban rail transit network \(G\), network node traffic matrix \(Q=[q(1),q(2),\cdots q(t)\cdots q(N)]\).  
Output: The \(h_{i}^{t}\) index and \(g_{i}^{i}\) index of the node, where \(i\) is the node number.  
Step 1. Construct an urban rail transit network model \(G=(V,E)\);  
Step 2. Establish a passenger flow matrix \(Q_{m\times N}\) of the urban rail network based on the pre-processed passenger flow data;  
Step 3. Normalize the passenger flow matrix \(Q_{m\times N}\) using Equation (6) to obtain a standardized matrix \(X_{m\times N}\);  
Step 4. Calculate the correlation coefficient of the passenger flow between the two nodes using Equation (7), and establish a matrix of sample correlation coefficients \(R_{m\times m}(X)\);  
Step 5. Use Equation (8) to find the joint coefficient between the nodes, and obtain the joint coefficient matrix \(H_{m\times m}\) between the nodes;  
Step 6. For node \(i\), the order of \(h_{ij}\) index is in descending order, the sorting number after descending order is \(k(1\leq k\leq m)\), and the corresponding index is \(c_{k}^{i}(1\leq k\leq m)\);  
Step 7. The \(h\) index and \(g\) index are calculated separately until the conditions \(c_{k}^{i}<k\) and \(\sum_{k}c_{k}^{i}<k^{2}\) are satisfied respectively, then the \(h_{r}\) index and \(g_{r}\) index of node are output.