An Attribute–Relation Analytical Framework for Regional Carbon Emission Systems: Evidence from Counties in Shandong Province, China

Regional carbon emission systems evolve through the continuous interaction between local emission attributes and interregional spatial relationships. However, existing studies have largely examined the spatiotemporal evolution of carbon emissions and the formation of spatial association networks separately, leaving the relationship between these two dimensions insufficiently understood. To address this gap, this study develops an attribute–relation analytical framework and applies it to 136 counties in Shandong Province, China. By integrating spatial analysis, social network analysis (SNA), SHAP interpretation, and the quadratic assignment procedure (QAP), the study investigates the evolution of carbon emission attributes, the organization of spatial association networks, and the mechanisms governing both processes. The results show that carbon emissions increased continuously from 2000 to 2020, gradually forming a persistent dual-core agglomeration pattern centered on the Jiaodong Peninsula and the central Shandong industrial corridor. Meanwhile, the spatial association network evolved from a core–periphery structure toward a more interconnected and polycentric configuration. Carbon emission attributes were primarily driven by fixed asset investment, population size, and land-use structure, whereas network formation was more strongly associated with economic development and land-use efficiency. The proposed attribute–relation analytical framework provides a systems perspective for understanding the spatial correspondence between carbon emission attributes and spatial association networks, offering an integrated perspective on the spatial state and organizational structure of regional carbon emission systems. This framework providing theoretical support for differentiated and network-oriented carbon governance.