# 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
### Comparative Analysis  
Since the degree of centrality is not discriminative, the proposed node importance measurement results based on \(h_{r}\) index and \(g_{r}\) index are compared with the result that based on BC, CC, EC, PageRank (PR), full-day passenger inbound flow (PF). The top ten most important nodes based on various metrics are shown in Table 5.  
Calculate the intersection degree between the \(h_{r}\) index and the \(g_{r}\) index and the top ten most important nodes of other sequences, as shown in Figure 9.  
It can be seen that the maximum intersection degree of the \(h_{r}\) index and the betweenness centrality, the closeness centrality, and the full-day passenger inbound flow is 0.3. The minimum intersection degree of the \(h_{r}\) index and the eigenvector centrality and PageRank is 0.2. The maximum intersection degree of the \(g_{r}\) index and the closeness centrality and the full-day passenger inbound flow is 0.5. The intersection degree of index with the PageRank algorithm is at least 0.2. The \(h_{r}\) index and the \(g_{r}\) index have good intersection with the closeness centrality and full-day passenger inbound flow, but have a bad intersection with the PageRank algorithm. The closeness centrality reflects the topological characteristic of the network and the full-day passenger inbound flow shows the passenger flow characteristics of the network, which reflects the characteristics of the \(h_{r}\) index and the \(g_{r}\), that is to say, considering both the network topology and passenger flow characteristics, balancing and optimizing the two aspects. In addition to the PageRank algorithm, the intersection degree of \(g_{r}\) index and the betweenness centrality, the closeness centrality, the eigenvector centrality, and the full-day passenger inbound flow are better than the \(h_{r}\) index. In this respect, the \(g_{r}\) index has a small number of correlations with \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Sort** & \(h_{r}\) & \(g_{r}\) & **BC** & **CC** & **EC** & **PR** & **PF** \\ \hline
1 & 210 & 160 & 36 & 206 & 160 & 165 & 35 \\
2 & 183 & 179 & 35 & 205 & 20 & 160 & 154 \\
3 & 179 & 183 & 167 & 207 & 161 & 72 & 59 \\
4 & 160 & 160 & 75 & 204 & 167 & 154 & 80 \\
5 & 17 & 22 & 9 & 208 & 17 & 80 & 18 \\
6 & 20 & 17 & 74 & 28 & 42 & 172 & 20 \\
7 & 59 & 66 & 66 & 27 & 46 & 74 & 150 \\
8 & 80 & 128 & 131 & 29 & 18 & 122 & 128 \\
9 & 150 & 174 & 183 & 203 & 165 & 131 & 174 \\
10 & 128 & 154 & 49 & 209 & 59 & 116 & 22 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Calculation results of DC, BC, CC, EC, and PageRank for some nodes. Figure 9: Statistical values of intersection between the new index and the existing index. passenger flow, but the nodes with high correlation coefficients are fairer and the recognition effect is better. Figure 10 shows the relationship between the \(h_{r}\) index of the urban rail network nodes and the typical centrality metrics and full-day passenger inbound flow. Figure 11 shows the relationship between the \(g_{r}\) index of the urban rail network nodes and the typical centrality metrics and full-day passenger inbound flow. The \(h_{r}\) index and the \(g_{r}\) index have two metrics when measuring node importance: First, the nodes with strong correlation of the passenger flow space between the intersection nodes of the urban rail network are important. Second, the strength of the correlation must be kept above a certain \"scale\", and the node is judged to be important. This \"scale\" is the \(h_{r}\) index and the \(g_{r}\) index. In addition, the calculation process of the \(h_{r}\) index and the \(g_{r}\) index also includes a property. That is, when a node is implemented as a target node, other nodes in the network are treated as nodes adjacent to it. This adjacency is achieved by spatial correlation. In this sense, the \(h_{r}\) index and the \(g_{r}\) index also extend the concept of nodal degrees.