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Urban density is central to urban research and planning and can be defined in numerous ways. Most measures of urban density however are biased by arbitrary chosen spatial units at their denominator and ignore the relative location of elementary urban objects within those units. We solve these two problems by proposing a new graph-based density index which we apply to the case of buildings in Belgium. The method includes two main steps. First, a graph-based spatial descending hierarchical clustering (SDHC) delineates clusters of buildings with homogeneous inter-building distances. A Moran scatterplot and a maximum Cook's distance are used to prune the minimum spanning tree at each iteration of the SDHC. Second, within each cluster, the ratio of the number of buildings to the sum of inter-building distances is calculated. This density of buildings is thus defined independently of the definition of any basic spatial unit and preserves the built-up topology, i.e. the relative position of buildings. The method is parsimonious in parameters and can easily be transferred to other punctual objects or extended to account for additional attributes. [ABSTRACT FROM AUTHOR]

We present a model that simulates the growth of a metropolitan area on a 2D lattice. The model is dynamic and based on microeconomics. Households show preferences for nearby open spaces and neighbourhood density. They compete on the land market. They travel along a road network to access the CBD. A planner ensures the connectedness and maintenance of the road network. The spatial pattern of houses, green spaces and road network self-organises, emerging from agents individualistic decisions. We perform several simulations and vary residential preferences. Our results show morphologies and transition phases that are similar to Dieletric Breakdown Models (DBM). Such similarities were observed earlier by other authors, but we show here that it can be deducted from the functioning of the land market and thus explicitly connected to urban economic theory. [ABSTRACT FROM AUTHOR]