In this paper, we attempt to compare space syntax with spatial interaction. At one level, these two approaches to urban spatial structure are non-comparable. Space syntax is largely a descriptive technique for visualising spatial relations at the level of connections between places while spatial interaction is a predictive model that forecasts how much travel there will be between places. Space syntax articulates the system in terms of whether or not a physical link, usually at the level of the street, exists while spatial interaction predicts movements between all origins and destinations which are places often anchored in terms of the street network, but which at the level of prediction, assume connections between all places. Space syntax is grounded at a fine spatial scale while spatial interaction defines places as aggregates of activity in larger zones than the scale of the street system. The main output of space syntax is a connectivity matrix of step lengths between streets whereas in spatial interaction, such networks are predetermined, measurable in terms of Euclidean distance or generalised cost of travel, and the output is the volume of travel prior to this being assigned usually to a street network.
There is however a fundamental way of relating the implicit network graph of spatial interaction to the explicit planar graph of the street network. We begin by assuming the planar graph of the network is conceived of as a primal problem of spatial interaction while the dual graph linking streets in the planar graph is the graph which is used in space syntax. We exploit this duality and show how we can move easily between spatial interaction as the primal and space syntax as the dual. This is rooted in a more fundamental graph – the bipartite graph which is a list of streets/arcs and their intersections/nodes from which the primal and dual emerge naturally. We explore various accessibility measures and show how they relate and correlate. We then go one step further and consider how various processes of random walking take place in these networks examining the steady states of the primal and dual problems in terms of the likelihood of a random walker visiting any node or street. We thus define primal and dual Markov chains that enable us to generate these probabilities. This provides a basic framework for comparing primal and dual in comparing spatial interaction with space syntax. We illustrate these measures on simple and easy to articulate graphs, extending this to a synthetic network of nearest neighbour links in Greater London based on 699 nodes and 1972 symmetric ‘streets’ between zones. This is a preliminary attack on the problem of linking these two approaches although many challenges remain
