Dual graph representation of transport networks

The purpose of this paper is to describe the dual graph technique developed by the authors to represent transport networks. The method is intended to simplify the coding of complex transport networks to a considerable degree, particularly when there are turning restrictions, or when multiple transfers between modes or transit lines must be taken into account. A first section presents the traditional form in which transport networks are analytically represented, and describes the main problems that are confronted. In particular, the difficulty to represent prohibited turns is shown to be a major problem; when such a restriction is introduced, the representation of the network becomes increasingly complex and intractable, requiring a large number of fictitious links and nodes. A second section describes the dual graph technique in general terms, and shows how the network code remains simple, even if prohibited turns are introduced, completely avoiding fictitious links and the possibility of errors. A third section describes the way in which dual networks are constructed in formal terms. It is shown that the process of constructing the dual graph can be automated easily, becoming completely transparent to the model user. In a fourth section the method is extended to represent transit routes or, in general, multiple operators and modes. This is achieved by introducing further dimension to the dual network (multidimensional networks); the dual of very complex transit networks can also be automated, avoiding the need for fictitious nodes and links to represent transfer points. A final section draws the main conclusions and points out that dual graphs can be very useful for detailed traffic models. Brief references are made to other known methods to represent turn restrictions.