You may have spotted a recent article on the BBC News website reporting research that analysed the structure of subway networks from a mathematical point of view. In Glasgow, we have one of the oldest but also one of the simplest subway systems in the world; the subway systems for larger cities such as Moscow or Paris tend to be considerably more complicated and to have developed episodically over many years. Nevertheless, the study reported by the BBC [full paper here] claimed to find some interesting regularities in their structure.
Since our Department has a resident expert on network theory, Prof. Ernesto Estrada, I thought it would be interesting to get his view of this work. As usual when science is reported in the mainstream media, it turns out that the really interesting and novel bit isn’t flagged up quite as clearly as it might be. Here’s Professor Estrada’s summary in full:
The study entitled A long-time limit for world subway networks reports some interesting aspects of the the topological characteristics of subway networks in different parts of the world. By topological I mean here “structural” or “organisational”, that is, the way in which the stations are connected.
In my view some of the results reported here are expected by some obvious organisational structures imposed on subway networks. First, such networks are planar. That is, we can draw them in a plane without any intersection between the lines. Most complex networks are far from planar, so giving to subway networks some special features. Planar networks do not contain certain classes of subgraphs or structures, which also imposes certain restraints on the other network properties.
The core-periphery structure found so far is however more interesting. There are four universal classes of topological organisations which are possible for a given network according to the mathematical results published by Estrada in 2007. One of these classes is the core-periphery. However, networks with similar functions appear spread in these four classes. For instance, social networks can have a core-periphery structure or any of the other three possible classes. An exception appears to be subway networks which all belong to the core-periphery category. Another are proteins represented as networks which belong to the so-called class of “networks with holes”. The authors’ statement about the existence of “fundamental mechanisms, independent of historical and geographical differences” is very interesting taking into account that the most commonly used mechanisms for explaining network growth do not reproduce the characteristics of core-periphery networks, as Estrada has shown in the mentioned 2007 paper.
If you’re a Strathclyde student and this has whetted your appetite, you may like to know that Dr Knight and Prof. Estrada teach a fourth-year class called Introduction to Complex Networks. Prof. Estrada also has a recent book on the subject, though this is aimed at graduate rather than undergrdauate level.
Oh, and while we’re on the subject of subway networks, I’d like to give a plug to a wonderful project by Benedikt Groß and Hartmut Bohnacker to create a map of London which follows the spatial layout of the famous Tube map. You might like to ponder how you could define such a distortion in a mathematically “tidy” manner…
(DP, with thanks to EE)