Administrative boundaries and urban areas in Italy: a perspective from scaling laws

Delineating boundaries of urban areas is no easy task, due to the inherent complexity of the problem, heterogeneity of relevant data and little consensus on how to properly measure the results. Any such delineation must eventually be cast onto administrative boundaries, an essential requirement for real-world applications. In the effort of relating administrative and alternative boundaries, we investigated in Italy the validity of general scaling laws, such as the area-population relation, and proposed a practical application. Relying on open data for population, settlements and road networks, we showed the extent to which scaling relations hold for different boundaries for urban areas, and how they compare to each other. We considered, beside Italian municipalities, urban areas based on the idea of "natural cities", obtained using head/tail breaks of areas related to human mobility as an explicit indicator of existence of a city. Area-population data for administrative boundaries can be reconciled with scaling relations valid for both the world's cities data and with those obtained from natural cities, provided an effective area is adopted in place of polygon planimetric area of municipalities. We eventually proposed an aggregation of administrative units using the empirical scaling relation as an objective function for accepting or rejecting pairwise fusion of boundaries. We suggest considering such a method, along with expert considerations, as an additional tool for real-world urban planning as seen from the very general perspective of seemingly abstract scaling laws.