Matrix Methods for Connectivity and Reachability in Transportation Networks

This paper presents a matrix-based approach for modelling and analysing transportation networks using concepts from graph theory and linear algebra. The incidence matrix and its transformation into the adjacency matrix through the product MMT are employed to represent structural relationships within the network. Matrix operations and their powers are used to study both direct and indirect connectivity, while the reachability matrix provides an effective algebraic criterion for determining accessibility among nodes. The theoretical results establish a connection between matrix formulations and graph connectivity, offering a systematic framework for network analysis. The applicability of the proposed method is demonstrated through several transportation models, including regional and large-scale networks, where key hubs, connectivity patterns, and efficiency are identified. The study shows that matrix-based techniques provide a scalable and practical tool for transportation planning, route optimization, and analysis of complex network systems.