## 5 Discussion  
This study constructed four types of urban networks, including information, investment, high-speed rail, and highway networks, and analyzed the mixing patterns in Chinese urban agglomerations based on both structural features and socioeconomic attributes. Therefore, some of the issues identified in the relevant studies are summarized from three perspectives: node attribute distribution, mixing patterns, and distribution of network assortativity coefficients. Our analysis of the node attribute distribution revealed significant heterogeneity in cities' structural features and socioeconomic attributes. Based on this observed heterogeneity, this study proposed and tested two potential mixing patterns: disassortative mixing (centripetal mixing pattern) and assortative mixing (balanced mixing pattern). These findings align with previous studies, for instance, research showing how core cities in the Yangtze River Delta dominated regional economic activities [10], and [PERSON] demonstrated similar resource concentration patterns in the Chengdu-Chongqing Urban Agglomeration through network centrality analysis [14]. This network-based perspective provides a novel approach to understanding the formation mechanisms of urban agglomerations by quantitatively analyzing how cities of varying characteristics establish connections. Rather than merely identifying the hierarchical structure, this method reveals the underlying connection preferences in intercity relationships. In studying the mixing patterns of different urban agglomeration networks, our network-based approach revealed distinct connection preferences across different types of networks. Specifically, this study found that high-speed rail and highway networks generally show disassortative mixing (centripetal mixing pattern) in terms of socioeconomic attributes, particularly within urban agglomerations, indicating these infrastructure networks tend to connect cities with significant economic disparities. However, this pattern shows notable exceptions in three major urban agglomerations. In the Beijing-Tianjin-Hebei region, high-speed rail network planning prioritizes regional coordinated development over economic efficiency. The Yangtze River Delta's networks are designed primarily to serve as national comprehensive transportation corridors, while the ChengduChongqing urban agglomeration's development is largely shaped by the geographical constraints of the Sichuan Basin. These cases demonstrate that high-speed rail network development in urban agglomerations is influenced by national strategic objectives and regional coordination policies rather than purely socioeconomic disparities. In contrast to their socioeconomic mixing patterns, these networks display assortative features in terms of degree centrality, suggesting connections are more likely between cities with similar passenger flow levels or infrastructure scales. More importantly, our analysis of information and investment networks demonstrates different mixing patterns. Information networks show significant assortativity (balanced mixing pattern) in both GDP level and permanent resident population at the global scale, indicating information flows tend to occur between cities with similar socioeconomic attributes. In contrast, investment networks exhibit significant disassortative mixing (centripetal mixing pattern), particularly within urban agglomerations, suggesting capital tends to flow between cities of different economic scales. Previous studies have primarily focused on describing the hierarchical structure and spatial distribution of transportation networks or analyzing economic connection patterns separately [12; 34]. Indeed, different types of networks play distinct roles in constructing intercity relationships [14]. While traditional infrastructure networks primarily reflect regional planning that emphasizes economic complementarity between cities (centripetal mixing pattern), information and investment networks reveal more complex connection preferences.