On the problem of boundaries and scaling for urban street networks

Abstract

Urban morphology has presented significant intellectual challenges to mathematicians and physicists ever since the eighteenth century, when Euler first explored the famous Königsberg bridges problem. Many important regularities and scaling laws have been observed in urban studies, including Zipf's law and Gibrat's law, rendering cities attractive systems for analysis within statistical physics. Nevertheless, a broad consensus on how cities and their boundaries are defined is still lacking. Applying an elementary clustering technique to the street intersection space, we show that growth curves for the maximum cluster size of the largest cities in the UK and in California collapse to a single curve, namely the logistic. Subsequently, by introducing the concept of the condensation threshold, we show that natural boundaries of cities can be well defined in a universal way. This allows us to study and discuss systematically some of the regularities that are present in cities. We show that some scaling laws present consistent behaviour in space and time, thus suggesting the presence of common principles at the basis of the evolution of urban systems.

Robustness and closeness centrality for self-organized and planned cities

“…In particular, we could consider the ratio σ between the total length of the street network and the total length of its Delaunay triangulation as an intuitive measure of the street network efficiency in the primal space. Such a measure is not sensitive to the size of the net, as it was shown that the total street length L of a urban street network is consistent with a linear function of N , i.e., L(N ) ∝ N [25,33]. Then we find that σ London ≈ 0.36, σ Chicago ≈ 0.46, σ ERPG ≈ 0.65, σ GRID ≈ 0.59.…”

“…Chicago's street network has a relatively short history as it was incorporated as a city in 1837 and had a rapid expansion in the midnineteenth century, and its urban plan is mostly reticulate. In the case of Chicago, given the lack of an entity such as an orbital road, we consider the urban area surrounding Chicago as defined by the condensation threshold methodology [25].…”

Preserved layout features embedded in road network development

“…Klinkhamer et al [26] also observed a universal statistical behavior in the degree distributions of road networks under dual representation which is best represented as a power-law (Pareto) distribution with scaling exponent of −2.49. Masucci et al [32] observed a collapse of the cluster of road network elements vs spatial extent into a universal logistic growth, signifying a characteristic scale that leads to the giant connected cluster. Kirkley et al [33] even reported the invariance of the betweenness centrality distributions of road intersections, which is deemed to be a universal property of planar graphs.…”

General scores for accessibility and inequality measures in urban areas

“…Usually, studies about public transport analyze the networks of transport as static graphs, where the nodes represent stops and the edges represent the routes connecting them [16,17,18,19,20]. Very few studies have instead incorporated in a systematic way the "temporal" features of these systems [5,9,21], i.e., how users navigate through urban networks to reach their destinations.…”