## 1 Introduction
Mixing patterns are a fundamental metric in complex network theory that characterizes the tendency of network nodes to connect with others sharing similar or dissimilar attributes [17]. In the context of urban agglomeration studies, it quantitatively captures how cities with different socioeconomic attributes or structural features within urban agglomerations. Additionally, through the assortativity coefficient, it provides a mathematical framework to measure whether cities tend to connect with others of similar characteristics (assortative mixing) or different characteristics (disassortative mixing). Furthermore, mixing pattern analysis extends beyond simple connectivity measures by incorporating node attributes into network analysis, enabling a more nuanced understanding of how cities' socioeconomic attributes and structural features influence their interaction patterns within urban agglomerations. Thus, it reveals whether urban development follows patterns of homogeneous or heterogeneous clustering. It is crucial to understand the formation of relationships within the network and the structural evolution it undergoes. However, discussions remain limited regarding the revealing of intercity connection tendencies through structural features and socioeconomic attributes, as well as how these connection relationships influence the formation of urban agglomerations. Through analyzing selected urban agglomerations, this paper aims to recognize the mechanisms of relationship formation within urban agglomeration networks, quantitatively evaluate whether cities' socioeconomic attributes and structural features play consistent roles in shaping urban agglomeration networks, and develop an analytical framework based on assortativity coefficient distributions for classifying and assessing the diverse developmental patterns of urban agglomeration networks. The assortativity coefficient is used as the primary analytical metric to measure the mixing patterns of information, investment, high-speed rail, and highway networks in these seven urban agglomerations. The research examines the mixing patterns among urban agglomerations, revealing the connection tendencies of structural features and socioeconomic attributes. The main contributions of this research can be synthesized into three main aspects. First, this study examines multiple urban agglomerations and urban agglomeration networks. Second, this study reveals the mixing patterns in structural features and socioeconomic attributes of urban agglomeration networks by examining information flows, capital flows, human mobility, and infrastructure connectivity. Third, through statistical analysis of the assortativity coefficient distributions in urban agglomeration networks, this study discovers that they follow a stretched exponential distribution, with distribution parameters that can help identify mixing patterns and evaluate the development modes of urban agglomerations, thereby providing structured insights to support future planning strategies and optimize development policies for urban agglomerations. This paper continues as follows. Section 2 presents a literature review on the urban network and mixing pattern. Section 3 presents the method and data. Section 4 presents the results on the mixing pattern of urban agglomeration networks. Section 5 presents the discussions. Finally, Section 6 presents the conclusions.