Educational and digital territorial inequalities in Italy: a density-based clustering approach across Degree of Urbanization (DEGURBA) areas

Regional educational inequalities represent one of the main challenges to social cohesion and regional development in contemporary societies. In the Italian context, differences between urban, intermediate, and rural areas significantly influence access to educational services, cultural participation, and conditions of educational vulnerability. This study proposes a multidimensional analysis of educational and digital vulnerabilities in Italian areas classified according to the DEGURBA (Degree of Urbanization) typology. Using ISTAT territorial indicators, the paper constructs three conceptual frameworks related to: (i) educational and digital accessibility, (ii) cultural and social participation, and (iii) educational vulnerability. The empirical analysis is conducted using densitybased clustering algorithms (DBSCAN and HDBSCAN) to identify homogeneous territorial patterns and spatial configurations of educational disadvantage. The results highlight the existence of relatively stable territorial patterns across Italy, characterized by different combinations of educational isolation, weak digital infrastructure, low cultural participation, and educational vulnerability. A comparison between DBSCAN and HDBSCAN also reveals significant convergence in the structure of the identified clusters, suggesting the territorial robustness of the emerging profiles. Rural and peripheral areas tend to exhibit higher levels of educational disadvantage and lower accessibility to services, while urban areas display more heterogeneous and fragmented patterns. The paper contributes to the literature on educational inequalities and socio-spatial planning studies by proposing a multidimensional and spatially oriented framework for the analysis of territorial educational vulnerabilities.