A city is a large, permanent human settlement. But try and define it more carefully and you’ll soon run into trouble. A settlement that qualifies as a city in Sweden may not qualify in China, for example. And the reasons why one settlement is classified as a town while another as a city can sometimes seem almost arbitrary.

City planners know this problem well. They tend to define cities by administrative, legal or even historical boundaries that have little logic to them. Indeed, the same city can sometimes be defined in various different ways.

That causes all kinds of problems from counting the total population to working out who pays for the upkeep of the place. Which definition do you use?

Now help may be at hand thanks to the work of Bin Jiang and Yufan Miao at the University of Gävle in Sweden. These guys have found a way to use people’s location recorded by social media to define the boundaries of so-called natural cities which have a close resemblance to real cities in the US.

Jiang and Miao began with a dataset from the Brightkite social network, which was active between 2008 and 2010. The site encouraged users to log in with their location details so that they could see other users nearby. So the dataset consists of almost 3 million locations in the US and the dates on which they were logged.

To start off, Jiang and Miao simply placed a dot on a map at the location of each login. They then connected these dots to their neighbours to form triangles that end up covering the entire mainland US.

Next, they calculated the size of each triangle on the map and plotted this size distribution, which turns out to follow a power law. So there are lots of tiny triangles but only a few large ones.

Finally, the calculated the average size of the triangles and then coloured in all those that were smaller than average. The coloured areas are “natural cities”, say Jiang and Miao.

It’s easy to imagine that resulting map of triangles is of little value. But to the evident surprise of their researchers, it produces a pretty good approximation of the cities in the US. “We know little about why the procedure works so well but the resulting patterns suggest that the natural cities effectively capture the evolution of real cities,” they say.

That’s handy because it suddenly gives city planners a way to study and compare cities on a level playing field. It allows them to see how cities evolve and change over time too. And it gives them a way to analyse how cities in different parts of the world differ.

Of course, Jiang and Miao will want to find out why this approach reveals city structures in this way. That’s still something of a puzzle but the answer itself may provide an important insight into the nature of cities (or at least into the nature of this dataset).

A few days ago, this blog wrote about how a new science of cities is emerging from the analysis of big data. This is another example and expect to see more.

Ref: http://arxiv.org/abs/1401.6756: The Evolution of Natural Cities from the Perspective of Location-Based Social Media