Structure and function of networks
How can we slow down the spreading of disease? How can we make Internet faster and more reliable? How can we find important genes for different diseases? These are actually questions that statistical physics can help us answer. Statistical physics is the science of how macroscopic properties comes from the interactions between myriads of small units. In traditional physics these units are atoms or molecules, in the field of complex networks we study just about everything else.
Networks are all around us, all the time—from the Internet to the nervous system, from the global friendship network to biochemical reaction systems, from the Swedish power grid to chains of historical events. These systems are to some extent random but they also have regularities, network structure. The network structure can tell us both something about how the network has evolved and how dynamic systems (like disease spreading on social networks or IP traffic in the Internet) behave on the network.
A central task in the study of networks is to construct measures of network structure. One such measure tells us how many triangles there are in a network; for example three persons that all are friends in a friendship network. By such measuresInformation spreading in social networks we can categorize different real-world networks. Indeed, social networks often have many more triangles than expected from a completely random network of the same size. Then we can investigate which mechanisms that give the network this property. Can it be that people often introduce your friends to each other? We can also ask how the many triangles affect the spreading of rumors in social networks. If we (once again) compare to a random network, triangles turn out to have a slowing effect—if you tell some gossip to two of your friends, it does not matter, for the spreading of the rumor, that they know each other. But if they had some other friends instead of being friends of each other (so they would not form a triangle), the information could spread further.
We use methods like the example above to study many different systems in society, biology and technology. It is a very interdisciplinary area, connected by the network-based methods. The research questions usually come from the disciplines traditionally studying these questions. Naturally, we collaborate researchers of these fields—sociologists, biologists, engineers and computer scientists. A good network physicist needs not only to know simulation techniques and statistical methods, but should also be able to speak the languages of these other fields. To discuss problems with people of so different backgrounds is at the same time the most rewarding and frustrating part of our research.
Anyone interested in this research is most welcome to contact Petter Holme.