The Ideal Shape of Subway Systems

Is there an ideal shape for a subway system? Statistical physicist Marc Barthelemy and Camille Roth of France's National Center for Scientific Research analyzed subways of New York, Tokyo, London and other large cities in the world - with all their different topologies and geographies - have strikingly similar subway structures:

With equations used to study two-dimensional spatial networks, the class of network to which subways belong, the researchers turned stations and lines to a mathematics of nodes and branches. They repeated their analyses with data from each decade of a subway system’s history, and looked for underlying trends.
Patterns emerged: The core-and-branch topology, of course, and patterns more fine-grained. Roughly half the stations in any subway will be found on its outer branches rather than the core. The distance from a city’s center to its farthest terminus station is twice the diameter of the subway system’s core. This happens again and again.

“Many other shapes could be expected, such as a regular lattice,” said Barthelemy. “What we find surprising is that all these different cities, on different continents, with different histories and geographical constraints, lead finally to the same structure.”

Subway systems seem to gravitate towards these ratios organically, through a combination of planning, expedience, circumstance and socioeconomic fluctuation, say the researchers.

Brandon Keim of Wired reports: Link