No two subway systems have the same design. New York City’s haphazard rail system differs markedly from the highly organized Moscow Metro (above), or the tangled spaghetti of Tokyo’s subway network. Each system’s design is the result of many factors, including local geography, the city’s layout and traffic distribution, politics, culture and degree of urban planning.

“There’s an endless list of possible parameters that can influence the shape of a subway network,” says Marc Barthelemy, a theoretical physicist at France's Alternative Energies and Atomic Energy Commission.

But Barthelemy isn’t interested in the differences between subway systems—he wants to find out what they all have in common. In a paper published May 16 in the Journal of the Royal Society Interface, he and his co-authors concluded that the geometries of large subway networks are guided by simple, universal rules.

Some scientists think that subway networks are an emergent phenomenon of large cities; each network is the product of hundreds of rational but uncoordinated decisions that take place over many years. And whereas small cities rarely have subway networks, 25 percent of medium-sized cities (with populations between one million and two million) do have them. And all the world's megacities—those with populations of 10 million or more—have subway systems.

If subways are emergent properties of cities, Barthelemy says, “you can forget about details.” And that’s exactly what he did in this new study. His team analyzed the geometry of all of the subway networks in the world that possess more than 100 stations—including Barcelona, Beijing, Berlin, Chicago, London, Madrid, Mexico, Moscow, New York City, Osaka, Paris, Seoul, Shanghai, and Tokyo— without trying to control for differences in politics, population density, or planning. If subway development is governed by emergent properties, then those details are already encoded within the structures, he says.

To look at how each network evolved over time, the researchers compared the geometry of each fledgling system with its modern-day setup. The analysis reveals that “as these systems get larger and more mature, they converge on a similar topology,” says David Levinson, a transportation engineer at the University of Minnesota, who was not involved in the study.

The researchers uncovered three simple features that make subway system topologies similar all around the world.

First, subway networks can be divided into a core and branches, like a spider with many legs. The “core” typically sits beneath the city’s center, and its stations usually form a ring shape. The branches, which are more linear, extend outward from the core in many directions.  

Second, the branches tend to be about twice as long as the width of the core. The wider the core, the longer the branches. And subway systems with more stations tend to have more branches. The number of branches corresponds roughly with the square root of the number of stations. 

Last, an average of 20 percent of the stations in the core link two or more subway lines, allowing people to make transfers.

Barthelemy says his team does not know which factors are guiding subway networks to follow these general rules; perhaps the rules maximize efficiency. For example, too many branches or connections would be redundant and unnecessarily costly. In contrast, having too few branches would reduce the range of areas that the network services, and having too few connecting points would reduce travel efficiency.

Of course, local factors may cause some deviations from the rules. New York City’s subway system does not have a clearly defined ring-shaped core; Barthelemy thinks the reason may be that the core’s shape is constrained by the proximity of the East and Hudson rivers which surround the city center—the long, but narrow island of Manhattan.

The Moscow Metro is also something of an outlier, in that its branches are three times longer than the core, and 50 percent of its core stations connect multiple trains. Levinson chalks up these differences to strong Soviet-era central planning; in contrast, many of the other cities' networks were built by private companies in piecemeal fashion.

Nevertheless, Barthelemy contends that if local factors posed the most powerful influence on the shape of subway networks, then the team wouldn’t have discovered these universal rules. “To me, it means that there is some general mechanism that overcomes local details,” he says.

But, “the question is, how closely do they follow these rules?” Levinson asks. “If every city’s subway network had exactly the same features, it’d be obvious the rules were really strong.” Because they’re not all the same, it shows that local details also help to shape the network. Levinson says that it is also important to understand the source of those differences.

Barthelemy thinks the rules are universal, but are adapted to different environments. In future experiments, he plans to plug the newly discovered rules into simulations, applying them in different geographic contexts. If the rules are correct, he says, then simulating the growth of a network around a lake will produce a network similar to Chicago’s.

Understanding how subway networks grow and evolve might one day help to design better systems, Levinson says.