## 1 Introduction
Through qualitative analysis, factors such as urban economy, industry, population, infrastructure, and transportation were identified as critical in influencing the evolution of network structures in urban agglomerations during public health crises of an epidemic nature. Despite these advancements, certain limitations persist in analyzing the network structure of Chinese UAs during public disaster events. Presently, studies predominantly focus on scrutinizing the characteristics and influencing factors of individual UAs, with limited attention given to the classification and comparative analysis of multiple UAs. Furthermore, the temporal scope of research primarily centralizes before or during the normalization stage of COVID-19, with scant exploration of the post-epidemic phase [17; 18; 19]. Moreover, investigations into the factors influencing the network structure of UAs lean heavily towards qualitative research, lacking sufficient quantitative analyses of these influencing factors. Consequently, there is significant merit in categorizing the present developmental status of UAs in China and exploring the impact of public health disaster events on their network structure before, during, or after the COVID-19 stages [20]. This comprehensive approach is crucial for aiding UAs in managing subsequent similar disasters and fostering integrated development. Additionally, such research will be invaluable for government authorities and planners in optimizing resource allocation across various UAs around the world, facilitating targeted strategies to maximize benefits from cross-city cooperation [21; 22]. The outcomes of this study can provide a scientific basis for informed resource allocation and decision-making processes [23]. Presently, scholars primarily investigate the characteristics of UA network structures using complex network theory [24; 25]. Additionally, scholars employ network structure measurement methods, including the gravitational model and social network analysis, to scrutinize the characteristics of UA network structures [19; 26]. A key focus is the quantification of the hierarchical structure of city networks, which involves calculating city node indicators, including in-degree, out-degree, centrality, and intermediary centrality through centrality analysis [7; 27]. This method delineates the influence characteristics of node cities within UAs and the hierarchical features of the network structure. Linkage strength indicators between cities within the UA network are computed using social network analysis to reflect linkage characteristics, providing insights into the development and evolution patterns of UAs [28; 29]. Given the regional scale of UAs, data acquisition poses challenges. Scholars simplify and integrate traditional network structure research methods, selecting scientifically sound indicators to characterize UA networks, thereby enhancing the applicability of social network analysis [30; 31]. Characteristics of network structures, including connectivity, vulnerability, linkage, and hierarchy, are primarily measured, with UA network structures characterized by indicators of network connectivity and hierarchy due to the fixed nodes constituting the UA network. This study adopts a UA perspective, necessitating a comparison of network structure characteristics among different types of UAs during various epidemic periods and variations in influencing factors. By focusing on the connectivity and hierarchy, employing three representative indicators--degree of centrality, strength of network connections, and network density--through social network analysis, this approach ensures data accuracy, simplifies calculations, and effectively unveils the network structure characteristics of the UAs [32]. Moreover, the network structure of UAs represents a complex system subject to various influencing factors. Scholars have adopted a comprehensive approach drawing from traditional location theory, new economic geography, and relevant theories in evolutionary economic geography.