## 5 Discussion
These findings suggest that the mixing patterns of urban agglomerations are influenced by both network types and the underlying socioeconomic attributes of cities, offering a more nuanced understanding than previous structural analyses. In terms of the distribution of network assortativity coefficients, this study found that the structural and socioeconomic assortativity coefficients of urban agglomerations follow a stretched exponential distribution with unified parameters. This distribution pattern remains consistent across different urban agglomerations and network types, suggesting an underlying universal mechanism in the formation of urban connections. Previous studies have primarily identified the existence of core-periphery structures in urban agglomerations [16], but our analysis of assortativity coefficient distributions provides quantitative evidence for how these structures form. For instance, investment networks consistently show the lowest stretch parameter among all network types, indicating a stronger tendency toward disassortative mixing (centripetal mixing pattern). This finding extends beyond the traditional understanding of resource concentration by revealing how economic interactions favor connections between dissimilar cities. Interestingly, our analysis revealed variations in mixing patterns across different urban agglomerations. While the Yangtze River Delta shows stable differences in assortativity mixing, suggesting a more balanced network structure, the Guanzhong Plain exhibits larger variations and a more pronounced assortativity mixing (centripetal pattern). These distinctions indicate that urban agglomerations may develop different connection strategies despite similar core-periphery structures. Finally, the higher stretch parameters observed in information and high-speed rail networks suggest that peripheral cities actively participate in network formation rather than simply depending on core cities. The interaction between structural features and socioeconomic attributes in shaping network connections adds another layer to existing theories of urban agglomeration development. Consistent with other research [10; 14], our analysis demonstrates that infrastructure distribution and cities' structural positions play equally important roles in determining connection patterns. The distribution patterns of network assortativity coefficients and centripetal agglomeration modes revealed in this study provide the following practical implications for urban agglomeration planning and resource allocation:(i) Core cities in urban agglomerations demonstrate significant advantages in resource allocation. Therefore, during the development of urban agglomerations, governments should fully utilize the leading role of core cities by strengthening their connections with peripheral cities, promoting a rational flow of resources and economic activities, and achieving balanced regional development. (ii) Different types of networks in urban agglomerations exhibit distinct mixing patterns. In the construction of high-speed rail and highway networks, the impact of geographical location on urban relationships should be fully considered. Through the rational layout of transportation infrastructure, connections between peripheral cities is strengthened, enhancing their resource acquisition capabilities and providing a scientific basis for optimizing infrastructure layout. (iii) The structural and socioeconomic assortativity coefficients of urban agglomeration networks conform to a stretched exponential distribution with unified parameters. The unified distribution parameters derived in this study provide an effective tool for evaluating urban mixing patterns by comparing the distribution of assortativity coefficients across different urban agglomerations; characteristics of mixing patterns are identified, enabling governments to make targeted policy adjustments.