Topological necessity under terrain constraint: quantifying spatial configuration in a non-linear religious architectural complex at Fajie Temple, Songming, Yunnan

Space syntax has proven powerful for decoding spatial order in axially planned, wall-enclosed religious architecture, but its applicability to non-linear, terrain-embedded complexes without artificial boundaries remains untested. This study examines whether standard visibility graph analysis (VGA) metrics retain interpretive validity in such environments, using a multi-faith mountain religious complex in Southwest China as a revelatory case. VGA (2 m resolution) across the 14-building site yielded 25,729 valid grid cells. Integration is highly non-uniform (SHI_CV = 2.40, 95% CI [2.28, 2.52]) and strongly clustered in space (Moran’s I = 0.893, p = 0.001), concentrating at topographic choke-points rather than architectural centres. Pairwise comparisons show negligible effect sizes between religious groups, and exact Mann–Whitney U tests confirm no significant differences (all p ≥ 0.90): topographic position, rather than religious affiliation, is the leading correlate of integration. Intelligibility is critically low (R2 = 0.056, p < 0.001) and robust to GPS positioning error. These findings invert the standard interpretation of integration, as a measure of topographic passage necessity rather than deliberate spatial order, extending space syntax theory to geometrically unordered environments.