Optimisation of Bus Route Networks in Abuja Municipal Area Council Using Graph Theory

Urban mass transit in the Abuja Municipal Area Council, Federal Capital Territory in the North Central zone, faces structural inefficiencies including route duplication, inadequate coverage of peripheral settlements, and poor connectivity between major activity nodes. This study applies graph theory and network optimisation techniques to evaluate and redesign the existing bus route network operated by the Abuja Metropolitan Management Council. The road network is modelled as a weighted directed graph with 87 nodes representing bus stops and major intersections, and 214 edges weighted by average travel time and passenger demand. Dijkstra's algorithm is employed to identify shortest-path routes between high-demand origin-destination pairs, while the minimum spanning tree algorithm is used to determine the most cost-efficient backbone network structure. Passenger demand data were collected through on-board counts and smart card transaction records over a 30-day survey period. The optimised network design reduces average passenger travel time by 19 percent and eliminates 11 redundant route segments, while increasing coverage to six previously unserved settlements in Karu and Nyanya districts. Capital cost savings from route rationalisation are estimated at 340 million naira annually. The study demonstrates that graph-theoretic methods provide a rigorous and computationally tractable framework for transit network planning in rapidly growing Nigerian cities. Keywords: graph theory, route optimisation, Abuja transit, Dijkstra algorithm, network planning.