Random walks in urban graphs: A minimal model of movement

A framework for calculating a weighted random walk on an urban street segment network is described, and tested as a predictor of pedestrian and vehicle movement in London and the wider region. This paper has three aims. First, it proposes the simplest possible model of agency in that individuals have neither memory, goals nor knowledge of the network beyond street segments immediately visible at an intersection. Second, it attempts to reconcile two divergent approaches to urban analysis, graph centrality measures and agent simulation, by demonstrating properties of topological graphs emerge from the lowest level agent behaviour. Third, it aims for far faster computation of relevant features such as the foreground street network and prediction of movement than currently exists. The results show that the idealised random walk predicts observed movement as well as the best existing centrality measures, is several orders of magnitude faster to calculate, and may help to explain movement without perfect knowledge of the map, by demonstrating the street network is structured such that long range information on optimal paths correlates with geometrical features locally visible at each intersection.