Extraction and Implementation Prioritization of a Connected Network for Active Bike-Sharing Stations Using the Minimum Spanning Tree Algorithm: A Case Study of Mashhad Metropolis

Bike-sharing systems can effectively support urban mobility when stations and bicycle routes are connected through a continuous network. In Mashhad, however, parts of the cycling infrastructure have been developed in a fragmented manner, resulting in incomplete connectivity between active bike-sharing stations and existing bicycle routes. This study aimed to identify the minimum network required to connect active bike-sharing stations in Mashhad and to prioritize its routes based on travel demand. The methodology was based on network analysis, spatial data, and an origin–destination (OD) matrix derived from recorded trips. After refining the street network and matching active stations to valid network nodes, the network was converted into a graph. A Minimum Spanning Tree (MST) algorithm was then applied to identify the routes required to connect all active stations with the minimum total length. The OD matrix was subsequently assigned to the extracted network, and routes were classified into three implementation-priority levels according to the volume of trips they served. The results showed that the proposed network has a total length of 190.3 km, of which 48.9 km, 50.6 km, and 90.8 km fall into the first, second, and third priority levels, respectively. In addition, the beta index increased from 0.706 to 1.000, while the cyclomatic number decreased from 2 to 0, indicating the creation of a continuous network without independent cycles. The findings suggest that integrating the MST algorithm with an OD matrix provides a practical approach for identifying a minimum station-connection network and prioritizing routes for implementation.