# 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
### Accuracy Analysis  
Accuracy is used to evaluate the performance of the node importance measurement method. Accuracy refers to the proportion of the number of important nodes in the measurement result set. In order to calculate the accuracy of the node importance calculation method, it is necessary to know the order of importance of the nodes in the urban rail network in advance. Here, the accuracy of the  
Figure 7: Calculation result of the \(h_{r}\) index and \(g_{r}\) index of the nodes (**a**) Calculation result based on passenger flow in off peak hours; (**b**) Calculation result based on passenger flow in peak hours; (**c**) Calculation result based on full day passenger flow.  
urban rail network node importance degree proposed in the initial planning of the Beijing urban rail network planning is used.  
In the initial stage of urban rail network planning, if the proposed ranking result of node importance is set \(U\), the precision of ranking sequence \(X\) under \(top_{i}^{n}\) is expressed as follows:  
\[Pre(U,X,n)=\frac{card\Big{(}top_{U}^{n}\cap top_{X}^{n}\Big{)}}{n} \tag{14}\]  
For instance, assume that the first 10 node importance set \(U\) set in the initial planning stage is \(U=\{1,2,3,4,5,6,7,8,9,10\}\), the first 10 node importance sets calculated by \(h_{r}\) index is \(X=\{3,6,9,12,16,17,18,19,20,21\}\), then the intersection of two sets has three elements 3, 6, 9, \(Pre(U,X,10)\)\(=3/10=0.3\).  
The accuracy of the \(h_{r}\) index, the \(g_{r}\) index, and the centrality index from 40 to 240 is calculated by Equation (14), as shown in Table 4.  
The accuracy diagrams of different calculation methods for the variation from 40 to 240 are given, as shown in Figure 8.  
As can be seen from Figure 8: when \(k=40\), the measurement eigenvector centrality has the highest accuracy, and the \(g_{r}\) index is the second; when \(80\leq k\leq 160\), the closeness centrality has the highest accuracy, and the \(g_{r}\) index is the second; when \(k\geq 160\), the \(g_{r}\) index has the highest accuracy, and the \(h_{r}\) index is second. The feasibility of using \(g_{r}\) index and \(h_{r}\) index to analyze the importance of urban rail network nodes is illustrated. The more urban rail network nodes, the better the estimation results of \(g_{r}\) index and \(h_{r}\) index. The PageRank algorithm is applied to the urban rail network, and the node importance measurement accuracy is low.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Pre(\(U\),\(X\),\(n\))** & \(\mathbf{h_{r}}\) & \(\mathbf{g_{r}}\) & **BC** & **CC** & **EC** & **PR** \\ \hline \(n=40\) & 0.300 & 0.500 & 0.300 & 0.500 & 0.600 & 0.200 \\ \(n=80\) & 0.533 & 0.667 & 0.301 & 0.733 & 0.667 & 0.267 \\ \(n=120\) & 0.700 & 0.800 & 0.520 & 0.850 & 0.800 & 0.450 \\ \(n=160\) & 0.840 & 0.840 & 0.680 & 0.840 & 0.840 & 0.640 \\ \(n=200\) & 0.933 & 0.967 & 0.815 & 0.867 & 0.833 & 0.800 \\ \(n=240\) & 0.971 & 0.971 & 0.914 & 0.914 & 0.914 & 0.914 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Precision accuracy of different methods.  
Figure 8: Precision accuracy of different methods.