Toward a Multidimensional Nexus of Sustainable Urban Competitiveness: PCA-Based Spatio-Temporal and Network Analysis in China’s Beijing–Tianjin–Hebei “2 + 36” Urban Agglomeration

Understanding how sustainable urban competitiveness evolves within megaregions has become a central concern in urban and regional studies, particularly under the pressures of carbon neutrality, spatial inequality, and network-driven urbanization. This study develops a multidimensional framework to assess the sustainable competitiveness of cities in the Beijing–Tianjin–Hebei “2 + 36” urban agglomeration and examines its spatio-temporal evolution and relational structure. Using a 30-indicator system grounded in factor foundations, economic performance, innovation capacity, openness, and environmental livability, we construct a composite competitiveness index through principal component analysis (PCA). Kernel density estimation reveals a pattern of overall improvement accompanied by widening disparities, characterized by selective agglomeration and the emergence of a pronounced high-value tail. Spatial autocorrelation consistently indicates significant spatial dependence, while LISA analysis identifies persistent low–low clusters and limited spillover absorption around core cities. A modified gravity model further uncovers a transition from a linear, corridor-based linkage structure to a more polycentric and networked competitiveness system, albeit with enduring peripheral weak nodes. The study contributes theoretically by conceptualizing sustainable urban competitiveness as a multidimensional nexus shaped jointly by territorial attributes and relational network structures. It demonstrates that competitiveness dynamics in megaregions emerge from the interplay of hierarchical consolidation, spatial divergence, and network reconfiguration—challenging the traditional assumption of simple core-to-periphery diffusion. The findings offer broader global implications, showing that the Beijing–Tianjin–Hebei case mirrors worldwide megaregional patterns, where proximity alone is insufficient to ensure functional integration, and where coordinated governance, network embeddedness and sustainability transitions increasingly determine regional competitiveness. This research provides a comprehensive analytical foundation for understanding and governing megaregional competitiveness in the era of sustainable development.