# 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
### Node Importance Measurement Result Based on Network Centrality Index  
Calculate the degree centrality (DC), the betweenness centrality (BC), the closeness centrality (CC), the eigenvector centrality (EC), and the PageRank value of the road network node. The node importance is sorted and the results are shown in Table 3.  
According to the degree value, the greater the degree of node, the greater the importance, but the importance of the nodes in each class cannot be distinguished. BC, CC, EC, and PageRank distinguish the importance of nodes well, and use Gephi to get results, as shown in Figure 5.  
Figure 4: Node degree distribution of urban rail network: (**a**) Measurement results of node importance based on node degree; (**b**) Distribution characteristics of node degree in urban rail network.  
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline
**Nodes** & **DC** & **Ranking** & **BC** & **Ranking** & **CC** & **Ranking** & **EC** & **Ranking** & **PR** & **Ranking** \\  & & **Results** & **BC** & **Results** & **CC** & **Results** & **EC** & **Results** & **PR** & **Results** \\ \hline
2 & 2 & 35 & 210 & 179 & 0.0568 & 203 & 0.0785 & 211 & 0.0049 & 44 \\
16 & 2 & 35 & 904.25 & 124 & 0.0986 & 36 & 0.3471 & 63 & 0.0036 & 179 \\
58 & 2 & 35 & 413.81 & 168 & 0.0837 & 104 & 0.4423 & 33 & 0.0034 & 213 \\
95 & 2 & 35 & 1256.6 & 87 & 0.0835 & 105 & 0.2310 & 102 & 0.0038 & 155 \\
123 & 2 & 35 & 1108.5 & 107 & 0.0839 & 102 & 0.3582 & 58 & 0.0035 & 189 \\
199 & 2 & 35 & 418 & 158 & 0.0498 & 216 & 0.0993 & 202 & 0.0046 & 53 \\
225 & 2 & 35 & 1818 & 56 & 0.0650 & 185 & 0.1247 & 150 & 0.0042 & 106 \\
233 & 2 & 35 & 210 & 179 & 0.0435 & 227 & 0.0783 & 213 & 0.0049 & 39 \\
12 & 4 & 3 & 1886.9 & 53 & 0.0974 & 41 & 0.4396 & 35 & 0.0068 & 11 \\
20 & 4 & 3 & 1605.7 & 69 & 0.0917 & 69 & 0.8774 & 2 & 0.00657 & 16 \\
36 & 4 & 3 & 5543.4 & 1 & 0.0990 & 33 & 0.5511 & 18 & 0.00655 & 17 \\
49 & 4 & 3 & 4090 & 10 & 0.1014 & 25 & 0.5083 & 24 & 0.00652 & 19 \\
116 & 4 & 3 & 1741.5 & 62 & 0.0779 & 132 & 0.5285 & 22 & 0.00689 & 10 \\
183 & 4 & 3 & 4131.3 & 9 & 0.0859 & 91 & 0.6997 & 11 & 0.00647 & 21 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Calculation results of degree centrality (DC), betweenness centrality (BC), closeness centrality (CC), eigenvector centrality (EC), and PageRank for some nodes.  
Consider a graph of the BC, CC, EC, PageRank results of the nodes, as shown in Figure 5. It can be seen from the figure that although the BC, CC, EC, and PageRank values of the nodes are widely distributed, the respective recognition effects are quite different. It can be clearly seen that the nodes of the PageRank recognition result are nodes with large importance such as nodes 72 and 154, but the colors in Figure 5a-c are very light. The PageRank algorithm measures the degree of node importance by considering the degree of connection of the nodes. When the degree of the normal node is large in the undirected graph, the node is of great importance. The BC considers the shortest path. It is considered that the more the shortest path passing through a node, the more important the node is. It can be seen from the topology map of the urban rail network that node 72 is at the edge of the network, and the shortest path between the pair of nodes does not pass through it, so the BC is small. Also, due to the position of the edge, the average distance between node 72 and other nodes is large, so the CC is small. Neighbor nodes of node 72 are not very important, so the EC is not high. It is worth noting that node 206 is the most important node in the CC recognition result, and node 160 is the most important node in the CC recognition result.  
Figure 5: BC, CC, EC, PageRank (PR) node importance measurement results (Diameter and color shade represent the size of the value) (**a**) BC node importance; (**b**) CC node importance; (**c**) EC node importance; (**d**) PR node importance.  
most important node in the EC recognition result. The node with high EC importance is located in the central area of the network.