## 4 Results  
### Structural Features and Node Attribute Distribution  
This paper first calculates and summarizes the basic structural features of the four types of urban networks analyzed, as shown in Table 4.  
The information network has the largest number of links and the highest proportion of the largest connected component, indicating that most of the sample cities have formed dense informational relationships. In contrast, the investment network has the smallest number of links, and the proportion of the largest connected component is significantly lower than in other types of networks, indicating that the investment network's structure is sparse, with weaker investment ties between the sample cities and relatively dispersed investment relationships. For the high-speed rail and highway networks, the number of links for the high-speed rail network is slightly higher than those for the highway network. This suggests that the connections between sample cities based on high-speed rail services are stronger than those based on highway infrastructure. However, the similar levels of connectivity between cities in both types of networks indicate that the coverage of intercity relationships established by the two transportation systems does not show a significant difference. Furthermore, when comparing the average path lengths and clustering coefficients of the four types of networks with those of random networks, it is evident that none of the four networks exhibit a small-world phenomenon. Based on the description of the basic structural features above, this study further analyzes the structural features of the nodes in the four types of urban networks. This study implemented the maximum likelihood estimation (MLE) method using the lmfit package in Python 3.7 to fit their distribution fitting and evaluated the fitting results referenced [PERSON] et al. 's testing method [55]. The fitting results are shown in Figure 5.  
The empirical data fitting reveals that the degree centrality and betweenness centrality of the nodes in the four types of networks follow a stretched exponential distribution, as shown in Equation (7):  
\[P(x)\sim\exp[-(\lambda x)^{\beta}] \tag{7}\]  
This distribution is jointly regulated by the scale parameter \(\gamma\) and the stretch parameter \(\beta\) (also referred to as the shape parameter). Generally, the scale parameter controls the decay location of the distribution, while the stretch parameter controls the concentration tendency and decay rate of the distribution. In general, when the stretch parameter is greater than 1, it indicates that the distribution has a distinct concentration point, and a larger stretch parameter implies that the distribution is more concentrated in the tail. Therefore, in a stretched exponential distribution, the stretch parameter has a stronger interpretive significance for the distribution. The fitting results of the stretch parameter for the centrality distributions of the four types of networks are shown in Table 5. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Type**} & \multirow{2}{*}{**Number of Nodes**} & \multirow{2}{*}{**Number of Edges**} & \multirow{2}{*}{**Average Degree**} & \multirow{2}{*}{**Density**} & \multicolumn{2}{c}{**Proportion of the**} & \multirow{2}{*}{**Average Path Length**} & \multirow{2}{*}{**Average Clustering Coefficient**} \\  & & & & & & **Connected** & & \\  & & & & & **Component** & & \\ \hline Information & 137 & 2627 & 19.1752 & 0.1410 & 98.54\% & 2.2720 & 0.5801 \\ Investment & 137 & 528 & 3.8540 & 0.0283 & 52.55\% & 1.5795 & 0.1891 \\ High-speed rail & 137 & 1176 & 8.5839 & 0.1262 & 94.16\% & 2.2614 & 0.5176 \\ Highway & 137 & 918 & 6.7007 & 0.0985 & 94.89\% & 2.4361 & 0.5285 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Structural features of the four types of urban networks.