A long-time limit of world subway networks

Details A long-time limit of world subway networks A long-time limit of world subway networks

2011-05-26

arxiv.org/abs/1105.5294v2

Physics

Physics and Society

9 pages, 9 figures, revised version

Scientific paper

We study the temporal evolution of the structure of the world's largest subway networks in an exploratory manner. We show that, remarkably, all these networks converge to a shape which shares similar generic features despite their geographic and economic differences. This limiting shape is made of a core with branches radiating from it. For most of these networks, the average degree of a node (station) within the core has a value of order 2.5, slowly increasing with time and displaying small fluctuations around this value. The current proportion of branches represents about 40% of the total number of stations and the average diameter of branches is about twice the average radial extension of the core. Spatial measures such as the number of stations at a given distance to the barycenter display a first regime which grows as r^2 followed by another regime with different exponents, which eventually saturates. These results -- difficult to interpret in the framework of fractal geometry -- confirm and find a natural explanation in the geometric picture of this core and their branches: the first regime corresponds to a uniform core, while the second regime is controlled by the interstation spacing on branches. The existence of a unique network shape in the temporal limit suggests the existence of dominant, universal mechanisms governing the evolution of these structures.

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