Networks of networks

This week the Bath centre for "Networks and Collective Behaviour", of which I'm a member but by no means an official spokesman, had its official launch event. A fun two day meeting on "Uncertainty in interaction networks". For people such as myself who are in to statistical mechanics and the collective behaviour of systems with many parts, networks are a natural extension to what we do. It's a wonderfully interdisciplinary field with lots of cool problems to solve. Besides, networks is where I started out.

So, due to all this, my first few posts on my return from paternity leave might be networks based. From this week's meeting one thing that got me interested was people who are turning their attention to "multiplex networks". This is a word that means lots of things to me so to be more clear we're talking about separate networks that interact (this interaction is key). Usually it is assumed it is the same set of nodes with different sets of edges representing different relationships between them.

Cartoon of a multiplex network with two different types of link

An example given at the meeting was the power grid which is interacts with the water supply network and other services. Another example could be your social network where you distinguish between work colleagues and friends or family. Transport networks (for example bus and tube in London) will clearly interact in their function even though they are separate networks. 

Ginestra Bianconi from Queen Mary's gave a nice talk, in which she cited this PNAS on a network of computer gamers in a massively multiplayer online game. Data can be obtained for different types of interaction. Things such as friendship, trade, communication (positive) or enmity and attacks (negative). The authors claim that in order to properly understand the social structure one must consider all these different types on interaction. Among the things they found was that positive relationships tended to be clustered exponential networks whereas negative networks were not clustered and had powerlaw degree distributions. This means that a small number of players have a large number of negative connections. Also, different players had important roles in different networks. It certainly seems that with this extra layer of data one is in a better position to fully understand the network.

Ginestra's own work (in this EPL) was concerned with political affiliation networks. This imagined two networks representing social connections in two political parties. Nodes can be active in both networks but will tend to become inactive in the opposite network to their current opinion closer to an election. There is a stat-mech model where "tend to" is represented by a field (call it temperature) that couples to how happy a node is (call it energy). I'm going to come back to this theme.

I think multiplex networks are going to be really fun to work with. Seeing as networks are a useful simplification of reality multiplex networks seem to represent the next level of detail.