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….Subway systems seem to gravitate towards these ratios organically, through a combination of planning, expedience, circumstance and socioeconomic fluctuation, say the researchers.
What particularly fascinates me is the prevalence of particular ratios within transit systems, suggesting that subways scale in consistent ways as their host cities grow.