The backbone of a city

Recent studies have revealed the importance of centrality measures to analyze various spatial factors affecting human life in cities. Here we show how it is possible to extract the backbone of a city by deriving spanning trees based on edge betweenness and edge information. By using as sample cases the cities of Bologna and San Francisco, we show how the obtained trees are radically different from those based on edge lengths, and allow an extended comprehension of the “skeleton” of most important routes that so much affects pedestrian/vehicular flows, retail commerce vitality, land-use separation, urban crime and collective dynamical behaviours. PACS. 89.75.Fb Structures and organization in complex systems – 89.75.-k Complex systems Centrality is a fundamental concept in network analysis. The issue of structural centrality was introduced in the 40’s in the context of social systems, where it was assumed a relation between the location of an individual in the network and its influence in group processes [1]. Since then, various measures have been proposed over the years to quantify the importance of nodes and edges of a graph, and the concept of centrality has found many applications also in biology and technology [2–5]. In economic geography and in regional planning centrality has been dominating the scene especially since the Sixties and Seventies. This means that some places (cities, settlements) are more important than others because they are more “accessible”. Accessibility was intended as a centrality measure of the same kind of those developed in the field of structural sociology, with the difference that the geographic nature of elements in space was saved around a notion of metric distance [6]. In the field of urban design, a long-term effort has been spent in order to understand what urban streets and routes would constitute the ”skeleton” of a city. By using this term, we mean the chains of urban spaces that are most important for the connectedness, liveability and safety at the local scale [7,8], and its legibility in terms of human wayfinding [9]. More recently, these latter two approaches are seemingly merging together in the first clues of a cognitive/configurational theory [10]. After an in-depth investigation of both the topological (dual) [11] and spatial (primal) [12,13] graph representation of street networks, in this paper we provide a tool for the analysis of the backbone of a complex urban a e-mail: [email protected] system represented as a spatial (planar) graph. Such a tool is based on the mathematical concept of spanning trees, and on the efficiency of centrality measures in capturing the essential edges of a graph. Differently from previous applications of this same concept [14], we consider spatial networks instead of topological ones, so that our trees can be shown graphically on the city maps and can serve as a support in urban design and planning; moreover, we consider two different kinds of edge centrality measures, and we compare the obtained trees with the standard spanning trees based on minimizing the total lengths. In our approach, cities are represented as spatial networks (networks embedded in the real space), i.e. networks whose nodes occupy a precise position in a twodimensional Euclidean space, and whose edges are real physical connections [5,15]. In such approach, 1-square mile samples of urban street patterns selected from reference [16] are transformed into spatial undirected graphs by mapping the intersections into the graph nodes and the roads into links between nodes [12,13]. Here we will focus, in particular, on the cities of Bologna and San Francisco as examples of two different classes of urban street patterns. The network of the former evolved over a long period of time through a self-organized organic uncoordinated contribution of countless historical agents while the latter is a mostly planned fabric built in a relatively short period of time following the ideas of one coordinating historical agent. Each of the two obtained graphs is denoted as G ≡ G(N,K), where N and K are, respectively, the number of nodes and links in the graph. In the case of Bologna we have N = 541 and K = 773, while in the case of San Francisco the same amount of 1-square mile 222 The European Physical Journal B