## 1 Introduction  
In the context of accelerating economic globalization and deepening regional economic integration, projections indicate that urban areas will accommodate approximately 68 percent of the global population by 2050 [1]. Cities have evolved beyond being mere centers of human mobility, information flow, and capital flow; they have become crucial hubs for global innovation, cultural exchange, and economic growth. The interactions between these cities, facilitated by the flow of critical elements, have resulted in a trend of spatial clustering. Consequently, establishing urban agglomerations as the dominant pattern of contemporary urban evolution [2, 3]. Urban agglomerations, representing an advanced stage of urban system development, have emerged globally as a model for regional development and spatial organization. They play a crucial role in regional industrial clustering, participation in global urban competition and cooperation, addressing various globalization challenges, and achieving regional economic integration [4, 5]. Regarding the evolution of urban agglomerations, traditional Central Place Theory and modern Flow Space Theory offer two distinct interpretative perspectives. Central Place Theory emphasizes urban hierarchical systems, suggesting that urban agglomerations form hierarchical spatial organizational structures centered around core cities through market coverage and economies of scale, where smaller cities become dependent on larger ones, resulting in spatial aggregation [6]. In contrast, Flow Space Theory transcends traditional hierarchical concepts, emphasizing that cities form functionally complementary spatial organizational patterns through multidimensional network connections, including flows of human goods, capital, and information [7]. Comprehensively, Flow Space Theory provides a dynamic theoretical foundation for urban planning and regional development research, supporting the development of urban polycentricity and regional integration. Flow Space Theory effectively breaks through the physical spatial constraints on intercity interactions, allowing relationships within urban agglomerations to extend beyond simple hierarchical dependencies. This results in the coexistence of cooperation and competition among cities, jointly promoting regional economic integration. Unraveling the underlying principles that shape these patterns is crucial for informing strategic decisions and policies that will guide the sustainable growth of urban agglomerations. Urban networks are an objective abstraction of the different types of relationships between cities. Structural analysis based on urban networks has become an essential analytical tool for understanding the interconnections and interdependencies among cities and revealing the evolution of regional economies. It is extensively applied in research related to urban agglomerations. Domestic and international scholars have used social network analysis (SNA) to conduct extensive research on urban agglomerations such as the Beijing-Tianjin-Hebei [8; 9], the Yangtze River Delta [10; 11; 12], the Pearl River Delta [13], and the Chengdu-Chongqing urban agglomeration [14; 15]. Moreover, there is often a consistent scaling relationship between the connectivity of cities in the network and the scale of the cities [14]. Because of urban economic, political, and cultural factors, urban agglomeration networks usually have a clear network center, which forms the center of a stable core-periphery structure [16]. The examination of urban agglomeration mechanisms is essential for understanding how cities evolve, both in their spatial developmental patterns and functional organization. While existing research has analyzed structural features across various types of networks in urban agglomerations, there remains a critical gap in understanding how cities with different attributes tend to cluster and establish connections within these networks.