## 4 Results
### Distribution of Network Assortativity Coefficients  
Based on the previous discussion of structural and socioeconomic assortativity in urban networks, to further analyze the general patterns of assortativity features in urban networks and explain the mixing patterns of urban agglomerations, this paper conducts a statistical analysis of the assortativity coefficients of different types of networks in the studied urban agglomerations, as shown in Figure 7. The fitting results revealed that while different perspectives estimate the assortativity coefficient distributions of urban agglomeration networks, the assortativity coefficients generally follow a stretched exponential distribution with a scale parameter (\(l=2.1556\)) and a stretch parameter (\(b=3.4906\)).  
The findings for different assortativity coefficients (Figure 7a) show that the structural assortativity coefficient and the socioeconomic assortativity coefficient have similar scale and stretch parameters, indicating that the mixing patterns of cities based on these two types of attributes are statistically consistent. On the one hand, this suggests that intercity relationships, whether in terms of structural features or socioeconomic attributes, exhibit a centripetal mixing pattern. On the other hand, it indicates a correlation between structural features and socioeconomic attributes. Based on the fitting results for different network types (Figure 7b), the scale parameters of the information and high-speed rail networks are similar to those of the global distribution, but they exhibit higher stretch parameters. As a result, urban agglomeration networks show that they are not related to each other. The investment network, however, has the lowest stretch parameter among the four network types, meaning that the assortativity coefficient for this network is more likely to be negative, and disassortativity features are more pronounced. This indicates that the investment  
Figure 7: Distribution and fitting of urban network assortativity coefficient: (**a**) different attributes; (**b**) different networks; (**c**) different urban agglomerations.  
relationships in urban agglomerations exhibit a stronger centripetal mixing pattern. Additionally, the stretch parameter for the highway network is slightly higher than the global distribution parameter, with the assortativity coefficients mainly concentrated within a fixed range. This suggests that disassortative features are evident in the highway networks of urban agglomerations, with a prominent centripetal mixing pattern for transportation infrastructure within the urban agglomerations. After fitting the assortativity coefficient distributions of different urban agglomerations (Figure 7c), the Guanzhong Plain urban agglomeration has the opposite trend to the Yangtze River Delta urban agglomeration: it has the highest stretch parameter but a relatively small-scale parameter. The Yangtze River Delta, an urban agglomeration network, has stable differences in assortativity coefficients that are not correlated with each other. On the other hand, the Guanzhong Plain urban agglomeration has larger differences in assortativity coefficients and a very clear centripetal mixing pattern. Further, for other urban agglomeration networks, the statistical results suggest that the distributions of assortativity coefficients are similar. Higher stretch parameters mean that the assortativity coefficients of the Chengdu-Chongqing, Middle Reaches of Yangtze River, and Central Plains urban agglomerations are more likely to be close to zero, showing that they are not related to each other. The parameters for the Beijing-Tianjin-Hebei and Greater Bay Area urban agglomerations are close to those of the global distribution. This means that they show disassortative features, which is in line with the centripetal mixing pattern.