Quantitative analysis of urban fabric in historic areas: graph-based case studies of Datong and Nanjing, China

Abstract The exploration of quantitative approaches to urban fabric, grounded in urban morphology theory, provides digital tools for accurately characterizing its physical attributes. Existing quantitative methods, however, have primarily focused on general morphological features such as dimension, shape, and density, leaving a gap in the development of methodologies targeting building types and their compositional relationships. In this study, two historical districts in China—Datong and Nanjing—are examined as case studies. By applying graph theory, we quantify the compositional patterns of urban fabric, defining plots, courtyards, and building typological units as nodes. This approach reveals the structural and typological differences between the two cases. The results demonstrate that integrating quantitative metrics such as building width, depth, and courtyard configuration with graph-theoretic indicators—including node degree and depth values—effectively uncovers distinct organizational patterns within the fabric. Furthermore, metric intervals derived from these indicators provide a means to differentiate the morphological characteristics of each district. This study highlights the potential of combining morphological analysis with graph theory to enhance the understanding of the complexity and diversity of urban fabric in historical contexts.