Network Analysis in Statistical Physics

Statistical Physics is a fundamental theory of many-body systems and it's also a central and fundamental theory of Complex Systems. In Statistical Physics, sometimes different systems with a totally different kind of interaction (relation between bodies in the system) can show some universal laws, and by common methods. These are important aspects of the value of Statistical Physics.

In Physics, traditionally, we apply statistical physics into physical systems, in which only physical interactions exist. However, numerous empirical and theoretical works imply that similar laws emergent from many different kinds of systems. So, to generalize concepts, methods and laws into general many-body systems should be an important task of new Statistical Physics.

Network Analysis is such an attempt to try to apply and abstract new ideas and concepts, to generalize the methods, and to investigate the properties in general interaction systems, and at last to find some universal rules for complex systems.

So any system which can be represented by vertex (bodies) and arcs (relations) between different vertexes is the object of Network Analysis. A series of common methods to measure and order the significance of vertexes and arcs, which is often named the centrality by social network analysts, have been founded. Also some new geometrical properties have been defined basing on real processes and physical models. Some works investigate the relation between structure and function of networks including the robustness, attack and disease control. Principle and knowledge about the construction and evolution is another important aspect of Network Analysis.

First, there is a review paper including some new ideas. It's prepared for usage in our own group. So it's written in Chinese and the English version will be available soon.

In the next part, we will discuss some ideas one by one in all these aspects.