Thursday, January 4, 2007

Topology of urban transportation networks

Dr. Efrat Blumenfeld-Lieberthal informed me of her recent research and agreed that I share it here. Efrat was my PhD student at the Technion. I am trying to persuade her to share my blogging chores on a regular basis. Here are Efrat's words...

There are two major contributions of the science of networks to transportation and urban systems. The first suggests that complex networks have the characteristics of small world networks, i.e. most nodes are neighbors of one another (have high clustering coefficient), but each node can be reached from all the other nodes by a small number of steps (short average path). The second contribution demonstrates that one of the best measures to characterize the nature of a network's morphology is the degree distribution of networks, which is the probability that each node has a specific number of links. It was found that in many types of complex systems the degree distribution obeys a power law. In other words, in complex systems there are few highly connected nodes and many nodes with low connectivity.

Cities are complex systems by their nature. Similarly to the organization of other complex systems (e.g. the WWW or the molecules in a cell) urban networks have no central force that affects their spatial structure. Thus, it is reasonable to assume that the spatial behavior of the components of urban systems would fit these characteristics of networks. In 2006 at the Centre for Advanced Spatial Analysis, at University College London I studied transportation networks of urban systems in different countries. I considered the cities as the nodes, while highways, railways, and air routes represented the links. I found that that these networks share some common characteristics. Apparently, the topology of the transportation networks revealed the type of economy to which they belonged (e.g. stages in the economic development of countries). The following figures present the number of links (degree) as a function of the clustering coefficient for different cities in different countries. This presentation indicates the connectivity levels of each city. It can be seen that all Western European countries present similar characteristics, while Poland and the USA behave differently.

Figure 1 – Germany

Figure 2 – Italy

Figure 3 – UK

Figure 4 – Poland

Figure 5 – USA

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