###### Abstract
For example, a metropolitan area usually refers to the extended area of a single city, where economic activities and population mobility are primarily concentrated in the core city and its suburban areas. A functional area, on the other hand, emphasizes the functional network characteristics that span administrative boundaries, such as transportation connections and economic integration. The concept of conurbation highlights the overlapping boundaries of multiple cities in geographic space, while urban agglomeration focuses on the networked structure formed through economic, social, and transportation linkages between cities. Moreover, the term economic functional area describes cross-regional development corridors driven primarily by economic activities characterized by high levels of industrial agglomeration. In contrast, a metropolitan region combines geographic and economic characteristics, typically including one or more urban centers and their surrounding functional areas [11, 12, 13, 14]. The definition of urban agglomeration boundaries involves multiple disciplinary fields, including spatial modeling, urban morphology, and regional economics. Spatial autocorrelation theory analyzes the similarity of geographic features, revealing spatial connections and boundary characteristics between cities [15]. For example, the Spatial Durbin Model (SDM) is widely used to examine the diffusion and spillover effects of economic activities within urban agglomerations [5]. At the same time, network theory conceptualizes urban agglomerations as complex networks composed of multiple nodes (cities) and edges (economic or transportation links), highlighting functional interactions and spatial structures between cities [16]. These theories provide important conceptual support for identifying the spatial boundaries of urban agglomerations. Traditionally, the spatial boundaries of urban agglomerations have been delineated based on administrative boundaries. However, this static approach often fails to accommodate the complex, dynamic interactions within urban agglomerations, primarily because administrative boundaries do not necessarily reflect the actual functional division and interactions within the agglomeration [17; 18]. Additionally, administrative boundaries overlook cross-regional economic activities and population mobility, leading to misinterpretations of the agglomeration's true spatial range and structure [19]. Thus, a more accurate identification of the spatial boundaries of urban agglomerations requires a comprehensive analysis based on multi-dimensional data, including economic activity, population distribution, and mobility. The spatial range of urban agglomerations is closely linked to economic development and population mobility. The concentration and expansion of economic activities drive the spatial range of urban agglomerations, impacting not only the physical expansion but also the layout of functional zones [20; 21]. Economic activities such as industrial distribution and infrastructure investment directly influence the direction and scale of urban agglomeration delineation. Analyzing economic factors can reveal the levels of economic activity in different areas of the agglomeration, thereby identifying the spatial and temporal trends in its boundary shifts [22; 23]. On the other hand, population plays an equally crucial role in defining the spatial range of urban agglomerations [24]. Firstly, changes in the resident population reflect long-term settlement and concentration of economic activities within the agglomeration, influencing functional zoning and determining the core structure of the agglomeration [25]. Secondly, the mobility of the population through migration reveals economic connections between regions, prompting dynamic adjustments in the spatial boundaries of urban agglomerations [26]. Therefore, in the development of urban agglomerations, the interaction between economic growth and population dynamics determines both the scale and direction of the spatial range.