Applications of Graph Theory and Network Science to Transit Network Design

Abstract While the network nature of public transportation systems is well known, the study of their design from a topological/geometric perspective remains relatively limited. From the work of Euler in the 1750s to the discovery of scale-free networks in the late 1990s, the goal of this paper is to review the topical literature that applied concepts of graph theory and network science. After briefly introducing the origins of graph theory, we review early indicators developed to study transport networks, which notably includes the works of Garrison and Marble, and Kansky. Afterwards, we examine network indicators and characteristics developed to study transit systems specifically, in particular by reviewing the works of Vuchic and Musso. Subsequently, we introduce the concepts of small-worlds and scale-free networks from the emerging field network science, and review early applications to transit networks. Finally, we identify three challenges that will need to be addressed in the future. As transit systems are likely to grow in the world, the study of their network feature could be of substantial help to planners so as to better design the transit systems of tomorrow, but much work lies ahead.