Assessing Urban Sprawl Sustainability through a Composite Compactness–Connectivity Index: Evidence from Erbil, Iraq

Urban sprawl, marked by low-density development, fragmented land use, and automobile-dependent growth, remains a critical barrier to sustainable urban planning. This study develops the Sprawl Centrality Index (SCI), a composite diagnostic tool that integrates spatial compactness with network connectivity to evaluate the sustainability of urban form. Compactness was quantified using convex hull ratios of building footprints, while network connectivity was assessed through betweenness and closeness centrality derived from OpenStreetMap street data. The SCI was applied to 15 observation points across five urban zones in Erbil, Iraq, and validated against average network travel distances to hospitals. The results revealed clear spatial variation: central zones recorded SCI values of 0.8–1.2 with average travel distances of 3.6–4.0 km, whereas peripheral zones reached SCI values of 1.8–2.0 and average travel distances exceeding 9.0–12.0 km. Regression analysis showed a strong positive correlation between the SCI and accessibility ( R 2 = 0.747, P < 0.001), with compactness and betweenness emerging as the strongest predictors. The findings underscore the utility of the SCI as a low-cost, transferable framework for diagnosing sprawl-prone areas and guiding targeted planning interventions. By unifying spatial and functional metrics, the SCI equips planners with a robust, evidence-based tool for promoting compact, connected, and sustainable urban development.