## 1 Introduction  
Urban agglomerations (UAs) are important carriers of economic accumulation, industrialization, and urbanization. These spatial entities are characterized by complex networks and connections that collectively define the structural network of UAs [1, 2]. Previous studies have demonstrated that UAs possess strong spatial interdependencies and intricate interconnections among constituent cities, displaying network structures akin to those observed in complex networks [2, 3, 4]. The evolution of these network structures reflects the underlying economic and social development trajectories within these agglomerations [5]. Therefore, investigating the characteristics of UA network structures is of paramount importance. It enhances our understanding of inter-city relationships and development dynamics, providing insights into the cooperation mechanisms and resource synergies within UAs [6]. Such understanding is crucial for promoting the integrated regional development of urban agglomerations [7]. The 19 distinct UAs in China each display unique developmental characteristics influenced by geographical, demographic, industrial, economic, and other factors [8, 9]. These agglomerations encompass well-established international hubs like the Yangtze River Delta (YRD), Beijing-Tianjin-Hebei (BTH), and the Pearl River Delta (PRD), alongside others in the early stages of development, characterized by substantial disparities in their developmental statuses and potentials. Consequently, the analysis of Chinese UAs necessitates the consideration of the spatial network attributes of each UA. Therefore, the study of China's UAs needs to take into account the characteristics of the spatial network within these regions and summarize the development laws of the network structures across different types of UAs through a comprehensive generalization and analysis. Various countries and regions worldwide face the consequences of various public health disasters, including SARS, Ebola, influenza A, avian influenza, and COVID-19 [10; 11; 12]. Consequently, scholarly investigations into urban networks under epidemic-type public health disasters predominantly center on city and inter-city networks during these periods [13]. Researchers construct models to elucidate the evolution patterns and characteristics of these networks, comparing structural features before and after public health disasters to substantiate their substantial impact on city aspects such as population, economy, and society, which consequently influence network structures [14; 15; 16]. Modeling the network structure of UAs during public health disasters elucidates their evolutionary laws and characteristics. Comparative analyses of network structure characteristics substantiate the significant impact on city aspects, subsequently influencing city network structures. Previous research on urban networks was limited by the short duration of epidemics, challenges in data collection, and issues with precision, relying primarily on traditional panel data or big data methodologies to examine structural characteristics and evolutionary patterns. The COVID-19 pandemic of 2020, however, presented a unique scenario in terms of duration and impact compared to previous public health crises. Its prolonged presence and severe consequences significantly altered the network structures of urban agglomerations (UAs) all over the world. In response to the pandemic, most countries engaged in stringent epidemic control measures and entered a phase of prolonged epidemic normalization, which, in China, concluded officially on 8 January 2023. This shift prompted by the epidemic led scholars to investigate the evolution of the network structures of China's UAs under the influence of the pandemic. These studies uncovered varying impacts of the epidemic on different UA networks.