The most common and most useful design paradigm for an urban metro system is radial. Subway lines should be running across the city, passing through city center with transfers to other radial lines; larger cities can also support a circumferential line, or for the largest megacities (like Moscow) two, and unless there are multiple circumferentials, every pair of lines should intersect with a transfer. For example, here is Prague:
There are three lines, meeting in a Soviet triangle, running from one side of city center to the other. Together with an intact tramway network, this boosts Prague’s annual urban rail ridership to around 830 million a year, which is 310/capita, a figure that isn’t far lower than Tokyo’s and is higher than anywhere else I can think of.
But in some cities – but not Prague – there’s a kink in the radial design. For example, here’s Kyiv, with planned expansion:
The three existing lines form a perfect Soviet triangle. Line 4, Podilsko-Vyhurivska, is under construction and radial as well. And then there is the under-construction eastern extension of Line 3, Syretsko-Pecherska, looping back to meet Line 1 at Darnytsia. This is not standard radial design. But it’s fully understandable given the situation of Kyiv.
Kyiv has a division into left-bank and right-bank Kyiv. The Dnipro is, with islets included, 1-2 km wide, one of the widest rivers of Europe. There are few bridges. The main of the city is on the right bank, but left-bank Kyiv has its own independent center around Darnytsia, encouraged by the city’s development plan precisely because the river is such an obstacle.
The river division is not universal. Prague doesn’t quite have it – the Vltava is 160-200 m wide and there are many bridge crossings, so even though city center grew along the right bank, much of the near-center is on the left bank. The city is also hilly enough that there’s no coherent left- vs. right-bank identity, and the streetcar system is sufficient to connect left-bank neighborhoods with each other without passing through city center.
Conversely, London does have this division. Bank terms are not used there – one says North and South London – but the situation is the same, even though the Thames at 250 meters is not much wider than the Vltava, and has many crossings as well. Nonetheless, a South London identity exists, defined by paucity of river crossings to East London (but not to Central or West London), and by its own centers at Waterloo and London Bridge.
As a result, the radial Underground network forms a coherent sub-network in South London. Just as the Kyiv Metro is planned to feature a loop back on Line 3 in left-bank Kyiv starting 2023, London built the Victoria line to swerve east to cross each trunk of the Northern line twice, once in North London and once in South London, and the crossing with the main line at Stockwell is even cross-platform. Unfortunately, the South London crossing with the Battersea extension is without a transfer, a deliberate design decision made to reduce ridership and perhaps reduce crowding on the Vic.
Finally, New York should think explicitly in terms of right- and wrong-side parts of the city, the right side referring to city center, that is Manhattan. New York’s subway network is not radial, but the same principles apply just the same. There is a strong wrong-side identity for Brooklyn, and historically Downtown Brooklyn was a very large business center; today it remains near-tied with Long Island City for largest job center in the region outside Manhattan. Early-20th century designers did not think in such comparative terms but they understood that it was valuable to connect Brooklyn homes with Brooklyn jobs, and thus most subway lines in Brooklyn converge on Downtown Brooklyn, and only the J/M/Z and the L go directly from Williamsburg to Manhattan.
By a fluke, all four subway lines in Queens connect to Manhattan via Long Island City, the nearest neighborhood to Midtown. Thus, a business center emerged there, growing to rival Downtown Brooklyn; just as the city’s geography can create a subway network, the subway network can create the city’s geography.