ar X iv : 0 71 0 . 15 92 v 2 [ ph ys ic s . so c - ph ] 3 1 O ct 2 00 7 Scale - free Segregation in Transport Networks

Every route of a transport network approaching equilibrium can be represented by a vector of Euclidean space which length quantifies its segregation from the rest of the graph. We have empirically observed that the distribution of lengths over the edge connectivity in many transport networks exhibits scaling invariance phenomenon. We give an example of the canal network of Veneice to demonstrate our result. The method is applicable to any transport network. Transport networks are used to model the flow of commodity, information, viruses, opinions, or traffic. They typically represent the networks of roads, streets, pipes, aqueducts, power lines, or nearly any structure which permits either vehicular movement or flow of some commodity, products, goods or service. The major aim of the analysis is to determine the structure and properties of transport networks that are important for the emergence of complex flow patterns of vehicles (or pedestrians) through the network such as the Braess paradox [1]. This counter-intuitive phenomenon occurs when adding more resources to a transportation network (say, a new road or a bridge) worsens the quality of traffic by creating longer delays for the drivers, rather than alleviate it. The Braess paradox has been observed in the street traffic of New York City and Stuttgart, [2]. In the present Letter, we show that while approaching equilibrium, a transport network can be embedded into Euclidean space R N −1 , N being a number of vertices. Then, every edge of the network is represented by a vector which length quantifies its segregation from the rest of the graph. We have empirically observed that the distribution of lengths over the edge connectivity in urban transport networks exhibits scaling invariance phenomenon. The relation between the connectivity of city spaces and their cen-trality known as intelligibility is a key determinant of human behaviors in urban environments, [3]. In most of researches devoted to the improving of transport networks, a primary graph representation of urban networks is used in which streets and routes are considered as edges of a planar graph, while the traffic end points and street junctions are treated as nodes. The usual city map based on Euclidean geometry can be considered as an example of primary city graphs. However, another graph representation can be useful if we are interested in describing the transport network at equilibrium.