Spatial localization of closeness and betweenness measures: a self-contradictory but useful form of network analysis

Spatial localisation of closeness and betweenness measures: a self-contradictory but useful form of network analysis Closeness and betweenness are forms of spatial network analysis grounded in a long standing tradition of measuring accessibility and flow potential. More recently, these measures have been enhanced by the concept of spatial localisation, producing effective models for the prediction of pedestrian and vehicle driver behaviour. A contradiction arises where the distance metric used to define locality does not match the distance metric used to define shortest paths for closeness and betweenness. A typical case is the use of angular shortest paths within a Euclidean buffer as a pedestrian flow model. Such a model assumes that people make a mode choice based on distance, but a route choice based on least angular change – even when this results in an excessively long " problem route " , which conflicts with their criterion for mode choice. This study examines the prevalence of problem routes and the magnitude of their effect on some pedestrian and vehicle models. We show that while in a weighted analysis, pathological cases could invalidate an entire model, in the models presented the effect of this contradiction is minor. We do this by comparing model predictions to real flow data, using four strategies for handling problem routes: ignore, discard, reroute and strict locality. Strict locality is justified on grounds of bounded rationality. We find all strategies to give broadly similar results, although the reroute and strict strategies give marginally better simulation accuracy. We also present a discussion of the characteristics of each strategy, and findings on computational efficiency. We conclude that it is prudent in any computation of localised closeness and betweenness to consider the impact of problem routes; however they do not necessarily invalidate these forms of analysis, which remain useful. 1. Introduction Closeness and betweenness are measures of network accessibility and flow potential based on the telecommunications work of Shimbel (1953) and Freeman (1977). Each measures a form of centrality based on shortest paths through the network; with closeness measuring potential for " to-movement " while betweenness measuring " through-movement ". Modern implementations of these algorithms on spatial networks use a variety of distance metrics to define the shortest paths. Metrics may, for example, be Euclidean (minimizing the number of metres travelled along the network), angular (minimizing the cumulative angle turned along each route), topological (minimizing the number of nodes) or …