## 4 Case Analysis
### Calculation of Comprehensive Node Importance Evaluation Value  
Based on Equations (15) and (16), the matrix is normalized. According to Equations (17)-(19), the comprehensive importance evaluation value of each node in the coal-iron-water combined transport network is calculated and used as the node importance ranking. Research shows that if 15-20% of the key nodes in a network fail, the network will become paralyzed. Therefore, this paper lists nodes with the top 20% of comprehensive importance, as shown in Table 4.  
Finally, the node importance topology is plotted based on the calculation results. The larger and darker the node, the higher its importance. As shown in Figure 5, the comprehensive evaluation results are highly consistent with the complex network topology indicators. Nodes with larger degree and betweenness values are generally more critical and essential and require special protection and maintenance. However, ports like Jingtang Port (3) and Qinhuangdao (17), which have larger maritime transport volumes than rail transport, also need special attention. Furthermore, intermediate nodes like Yuanping (76), Macheng (36), and Suning (28) can't be overlooked. They effectively connect inland coal mines and central railway lines and hold a significant position in the coal transport network.  
\begin{table}
\begin{tabular}{c c c c c c} \hline  & **Node** & **Degree** & **Betweenness** & **Clustering Coefficient** & **Closeness Centrality** & **Importance** \\ \hline
**79** & Shanghai & 8 & 0.060963036 & 0.321428571 & 0.258566978 & 0.686753598 \\
**42** & Tianjin & 8 & 0.199926829 & 0.25 & 0.27852349 & 0.681208111 \\
**3** & Jingtang Port & 5 & 0.00753872 & 0.4 & 0.238505747 & 0.670792346 \\
**21** & Ningbo & 7 & 0.039638435 & 0.285714286 & 0.251515152 & 0.625456251 \\
**78** & Hefei & 5 & 0.076080383 & 0.3 & 0.231843575 & 0.621380689 \\
**76** & Yuanping & 3 & 0.053550659 & 0.33333333 & 0.236467236 & 0.614669238 \\
**17** & Qinhuangdao & 8 & 0.114059577 & 0.214285714 & 0.255384615 & 0.581799947 \\
**37** & Macheng & 3 & 0.007026713 & 0.33333333 & 0.198090692 & 0.571283504 \\
**11** & Nanjing & 5 & 0.049207013 & 0.2 & 0.239884939 & 0.48398803 \\
**16** & Nantong & 6 & 0.024352186 & 0.2 & 0.228650138 & 0.482679645 \\
**4** & Beijing & 7 & 0.357347351 & 0.047619048 & 0.284246575 & 0.46781698 \\
**62** & Xuzhou & 5 & 0.030384287 & 0.2 & 0.222520107 & 0.464014772 \\
**28** & Suning & 4 & 0.03107626 & 0.166666667 & 0.23782235 & 0.414215146 \\
**81** & Wuhan & 4 & 0.038749177 & 0.166666667 & 0.220159151 & 0.400494313 \\
**72** & Hangzhou & 4 & 0.0199362 & 0.166666667 & 0.224932249 & 0.399612576 \\
**33** & Jiujiang & 4 & 0.019723843 & 0.166666667 & 0.212276215 & 0.388402187 \\ \hline \end{tabular}
\end{table}
Table 4: Table of importance ranking of coal-rail-water intermodal transport network nodes (top 20%).  
\begin{table}
\begin{tabular}{c c c} \hline  & **Node** & **Importance** \\ \hline
**6** & Shanhaiguan & 0.189919413 \\
**7** & Liaocheng & 0.237802713 \\
**8** & Ankang & 0.066450504 \\
**9** & Chifeng & 0.312029063 \\
**10** & Manzhouli & 0 \\
**11** & Nanjing & 0.483998803 \\
**12** & Jiaozuo & 0.178951363 \\
**13** & Handan & 0.271262416 \\  &... & 0.400494313 \\
**82** & Tangshan & 0.244860113 \\
**83** & Hohhot & 0.140081314 \\ \hline \end{tabular}
\end{table}
Table 3: _Cont._