Constructing and Validating a Geometric–Organic Index for Road Networks in Qing Dynasty County Cities

The position of urban road networks along the spectrum from geometric order to organic growth reflects the long-term tension between institutional planning and adaptive accommodation to local conditions, yet systematic quantification of this continuum in large historical urban datasets remains absent. This study digitizes road network data for 256 Qing Dynasty county cities using GIS methods and proposes a Geometric–Organic Index (GOI), a composite measure formed by equal-weight averaging of four sub-indicators: cross-junction ratio (CrossR), orientation regularity (OrientR), block regularity (BlockR), and connectivity ratio (ConnR). The results show that the GOI follows a continuous unimodal distribution (mean 0.346, median 0.341, n = 220, representing cities for which all four sub-indicators including block regularity could be computed), confirming that the geometric–organic dimension constitutes a continuum rather than a binary classification. Across the 182 cities for which both GOI values and external city wall regularity scores are simultaneously available, wall regularity correlates significantly with road network GOI (Pearson r = 0.320, p < 0.001). Mediation analysis reveals that topographic relief influences road network structure indirectly through wall regularity (Sobel z = −2.15, p = 0.032; Bootstrap 90% CI excludes zero), establishing city walls as morphological templates through which environmental constraints are transmitted to the urban interior. Primal-graph-based syntax-style validation on 173 cities (the 182-city set restricted to n_nodes ≥ 10 and available road files) further shows that GOI correlates significantly with intelligibility (r = 0.403, p < 0.001) and synergy (r = 0.463, p < 0.001), while mean local integration correlates negatively with GOI (r = −0.349), revealing a structural trade-off between global order and local efficiency. The equal-weight GOI scheme proves robust across 624 weighting combinations (Kendall τ = 0.928 for near-equal-weight combinations), and a global spatial autocorrelation test (Moran’s I = 0.137, p = 0.001) indicates weak spatial clustering without undermining the principal conclusions. This study provides the first large-sample empirical test of the morphological transmission hypothesis linking a city’s outer boundary to its interior road network, and offers a transferable quantitative framework for urban morphological typology.