A New Theory of Space Syntax1

Relations between different components of urban structure are often measured in a literal manner, along streets for example, the usual representation being routes between junctions which form the nodes of an equivalent planar graph. A popular variant on this theme – space syntax – treats these routes as streets containing one or more junctions, with the equivalent graph representation being more abstract, based on relations between the streets which themselves are treated as nodes. In this paper, we articulate space syntax as a specific case of relations between any two sets, in this case, streets and their junctions, from which we derive two related representations. The first or primal problem is traditional space syntax based on relations between streets through their junctions; the second or dual problem is the more usual morphological representation of relations between junctions through their streets. The unifying framework that we propose suggests we shift our focus from the primal problem where accessibility or distance is associated with lines or streets, to the dual problem where accessibility is associated with points or junctions. This traditiona