## 4 Results
### Structural Features and Node Attribute Distribution
The results indicate that the stretch parameters for both degree centrality and betweenness centrality in the investment network are less than 1, suggesting that a large number of cities have low investment levels and investment control capabilities, with capital and investment being controlled by an extremely small scale of cities. Additionally, the stretch parameters for betweenness centrality in the information, high-speed rail, and highway networks are close to 1, indicating that the differences in the control of information, traffic flow, and infrastructure resources among the sample cities are relatively similar. Furthermore, it is noteworthy that the stretch parameters for the degree centrality distribution in the information, high-speed rail, and highway networks are generally greater than 1, indicating that the degree centrality of cities in these networks tends to concentrate within a certain range, with similar values within that range. However, a few cities outside this range exhibit a significantly higher degree of centrality than other cities, suggesting that central cities in certain urban agglomerations, such as Beijing, Chongqing, and Wuhan, dominate more resources, leading to an uneven distribution of urban resources. In addition to analyzing the structural features of network nodes, this paper also conducts statistical  
Figure 5: Distribution of node attribute of urban networks: (**a**) degree centrality; (**b**) betweenness centrality. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Type** & **Degree Centrality** & **Betweenness Centrality** \\ \hline Information & 4.22 (Out-degree)/2.48 (In-degree) & 0.93 \\ Investment & 0.68 (Out-degree)/0.14 (In-degree) & 0.48 \\ High-speed rail & 2.63 & 1.05 \\ Highway & 3.08 & 1.27 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Results of fitting the stretched parameters of the centrality distribution of the four types of urban networks. analysis and fits the socioeconomic attributes distributions of the sample cities; the results are shown in Figure 6.  
The fitting results show that the GDP and permanent resident population of the sample cities follow a log-normal distribution, indicating that the distribution of cities' socioeconomic attributes is similar to their network structural features, both exhibiting heterogeneity. However, the log-normal distribution suggests that the differences in socioeconomic attributes, such as GDP and permanent resident population, among the sample cities share a degree of similarity, though relative differences between cities may be amplified by variations in economic levels. Moreover, it is observed from the distribution that a few cities in the tail of the distribution have socioeconomic attributes significantly higher than the fitted line. These cities are primarily concentrated in the Yangtze River Delta, the Greater Bay Area, and other central urban agglomerations, indicating that there are notable differences in socioeconomic attributes between central cities and other cities within the sample urban agglomerations. In summary, the statistical findings on the structural features and socioeconomic attributes of the sample cities suggest that these attributes can support two possible mixing patterns: disassortativity (centripetal agglomeration) and assortativity (balanced agglomeration). Therefore, this paper will further verify the two mixing patterns hypotheses by calculating the assortativity coefficients of urban agglomeration networks.