Global subway systems converge on common topologies

A paywalled paper in the Royal Society's journal Interface argues that the world's underground rail systems are all converging on an "ideal" form. The paper, "A long-time limit for world subway networks," shows that subway systems grow "organically," in response to the needs expressed by the cities above them over the course of decades, and reveal truths about the shape of cities. In Wired, Brandon Keim describes the findings:

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.

World’s Subways Converging on Ideal Form



    1. I think I learned somewhere that there are emergent patterns in road development as well.  Something about how prior to the automobile, cities grew in spokes along rail lines and waterways.  Then with cars and roads, you started to see concentric rings of growth rather than fattening spokes.

  1. Except in Toronto where we argue over subway plans for 20 years and then don’t build them

    1. nonono, first you build a new subway line to an Ikea.  Then, years later it is determined that one of Canada’s largest universities should maybe have subway access too.  But most importantly, Ikea gets the access first.

      1. Does a rail line extend to your International Airport? If so, be grateful: you are decades ahead of Melbourne. 

        1. IIRC a significant amount of IKEA’s earnings are not from the the large furniture boxed, but the small stuff in the halls directly before the checkout. 

        2.  I have seen folks coming back from Ikea in Toronto on the subway with a couch. Two large, tired looking men.

  2. It would make similar sense to say that most cross country rail systems worldwide adhere to “a common topology” – cross country track is generally stretched out straight over wide gently rolling swaths of landscape.

    Instead of saying that subways have global similarities, it makes more sense to say that large cities themselves adhere to a common topology. Generally speaking, London looks like Los Angeles looks like Tokyo. Their transit systems just happen to look nearly alike, because they ARE nearly alike.

      1. Even from just the snippet it’s a bit deeper than “cities have suburbs”. The form factor of the subway net (circle and spoke vs grid) abd especially the ratio of the inner to outer net are both – to me, at least – non-obvious things to be the same across multiple cities.

        1. A grid is your layout of choice if you desire minimum efficiency. Not terribly surprising that this isn’t what most cities choose.

        2. As @twianto:disqus said, the reason we don’t use a grid is because it would be horribly inefficient; unless people only go up and down and left and right.

          This is the layout that’s used because it’s the one that makes sense.

          Glad I’m not the only one who thought this all seemed a bit obvious.

          1. Surely it just validates the decisions of the transport people?

            That would be one interpretation. You could also argue that that the cities might have grown only to the maximum size that is sustainable by the transport network.

            (Is the nesting limit for comment replies ever going to get fixed?)

    1. I wonder if they look alike because they were built by the same people. You don’t just look at London’s underground system and say, “hey, that’s neat, let’s have a go at it.”. No, you hire the people who built London’s (they’re out of work, right? there’s only so much subway a city can afford each decade) and have them plan it out for you, then subcontract it out to your local construction industry. Cut copy paste. This isn’t like the space race, where you had two independent systems with almost no sharing of information.

      1. No.

        (I certainly hope that the people who built the London Underground in the late 1800s don’t have to work anymore.)

        1. Not to mention that the systems are often built over decades if not centuries. I mean, I imagine that the people who built the Jubilee Line Extension are still working- probably digging Crossrail. I agree that all of the builders of the original Underground are, well, underground by now.

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

    And, here in Atlanta, fear of black people.

    1.  I remember when they built and operated the first MARTA train.  I think it was all buses before that.

      1. It’s still a lot of buses. And in particular, suburban Cobb and Gwinnett counties both run their own bus lines whose sole purpose is to transport people from those counties to a MARTA station. MARTA has proposed extending the trains up into those counties on several occasions and the county governments have opposed it out of fear of crime (= fear of black people). By having separate systems with a restricted set of linkages, they believe they can more easily control the flow of criminals/black people into their counties. As if someone is going to take a three hour train ride to steal a TV and transport it back on the train. To this day, the only places where the train lines cross I-285 is where they can stay inside Fulton or Dekalb counties.

        And Republicans think racism is no longer a problem (except against white people).

        1. Yeah, I see that “what about racism towards white people?” line coming up quite a bit since that thing in Florida.  You think guys born into the most privileged group on earth would somehow appreciate it more.  But maybe, as the distribution of race in American society continues to shift,  they might live long enough to actually get a well deserved taste of it. 

          And that is interesting about how those attitudes effect MARTA routes.  I suspect some people out in those suburbs like having a car as a ‘barrier to entry’ for living there.

  4. Forget the paywall – the paper’s on arxiv:

  5. Look at my paper. I did a study and found that the words mean exactly what I said they meant when I designed the study. Statistics verify it.

  6. Well, at least the image is somewhat misleading, as the MAPS do look similar, but the maps are designed to convey routing information, not topological or pure geographic information.

  7. I suspect that the physical layouts exhibit even greater self-similarity than the maps; no human being would stack books like that.

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