Spatial Structure and Income Inequality in Iranian Provinces: A Cluster-Based Analysis of Complex Relationships

This study investigates the complex relationship between spatial structure and income inequality across Iran's 31 provinces, aiming to move beyond linear and simplistic analyses. The methodology is based on a two-stage quantitative approach: first, four key indicators—urban primacy, polycentricity, the Gini coefficient, and an expenditure dispersion index—were calculated for each province. Second, K-Means cluster analysis was used to classify provinces based on their spatial economic profiles. The findings reveal that no universal link exists between spatial form and inequality, uncovering several distinct patterns: 1) The Dominant Metropolis model (Tehran and Alborz), where extreme spatial concentration is coupled with acute inequality; 2) The "Polycentricity Paradox," where a similar spatial form leads to two contrasting outcomes: "efficient polycentricity" with low inequality (e.g., Kurdistan) and "inefficient polycentricity" with high inequality (e.g., Sistan and Baluchestan); and 3) The "Industrial Multi-Polar" model (Khuzestan), where a balanced spatial form coexists with high income inequality. The main conclusion is that physical form alone does not determine socio-economic outcomes; rather, the "functional quality" and "degree of integration" of the urban network are far more decisive. These findings underscore the need for context-specific regional policies focused on strengthening economic linkages between cities instead of merely engineering spatial form.