Addressing transportation challenges in Purwokerto: A graph theory approach to accessibility and sustainability

Rapid urbanization and growing private vehicle ownership have led to increasing congestion and declining transport efficiency in Indonesia's secondary cities. Purwokerto, as a medium-sized urban area, faces the challenge of balancing mobility needs with sustainability goals. This study aims to identify priority areas for integrated and sustainable transportation development using a spatial-network approach. Road network and land use data from OpenStreetMap (OSM) and Rupa Bumi Indonesia (RBI) were analyzed using Kernel Density Estimation (KDE) and Graph Theory to assess road density and accessibility. It shows a 37.8% increase in road network concentration between 2015 and 2025, extending from the urban core toward Kembaran, Sokaraja, and Patikraja. Graph analysis revealed that Sokaraja 1 and Patikraja have the highest accessibility indices (1.630–1.800). Urban center areas such as Purwokerto Timur, Purwokerto Utara, and Purwokerto Selatan show lower accessibility levels. The low ones also exist in peripheral areas such as Kembaran, Baturaden, reflecting opportunities for gradual, sustainable connectivity improvement. The research identifies a hierarchy of priority zones for transport development to promote equitable, sustainable mobility. The findings align with Sustainable Development Goal 11 (Sustainable Cities and Communities) and demonstrate how medium-sized cities can plan proactively toward integrated and low-carbon transportation systems.