Complex Networks in Statistical Physics

Jinshan Wu^{1, 2} and Zengru Di¹

1. Department of System Science at School of Management, Beijing Normal University, Beijing 100875, China

2. Department of Physics, Beijing Normal University, Beijing 100875, China

Abstract:

From the point view of Statistical Physics, Networks are many-body systems with general relations including physical and non-physical interaction. In this article, the authors review most of the main results and organized them by traditional logic of Statistical Physics, and some ideas for research works in the future is presented. According to the different property of interactions, Complex Networks are classified into three categories, undirected networks, directed networks and weighted networks. First, the definitions of some static geometrical quantities and their properties on such networks are collected, and some new static geometrical quantities are proposed on the basis of research works on construction and evaluation of mechanism model of networks. Second, we turn to the mechanism models. Most kinds of models are included there, while we point out that the mechanism of bi-scale-free networks is still waiting for our more attention. Development of networks is related closely with the mechanism model. Some of the works in this aspect are putted into the third part. Results in physical models on networks and the dynamical properties of networks are organized in the next section. In this part, the exploration on robustness, structure-function analysis and special properties of physical models such as random walk and Ising model should be extremely interested to physicists. Then we take two of our recent works--network of scientists in Econophysics and networks of physical input & output tables--as examples to demonstrate some initial application of networks analysis. At last, a brief introduction of the common analysis and numerical methods are listed for further reading. After all, Complex Networks, as an attempt to extend Statistical Physics into general systems, should be one of the central focuses of traditional researchers in Statistical Physics.

Keywords: Networks, Random Graph, Power Law, Scaling Law, Scale-free networks

All links will redirect into Chinese version. A full English version will be provide soon.

This review paper is rewritten from a Chinese version. Now only the abstract and table of contents is availuable in English, the full version will be provided in nearly future. Before that time, please see the Chinese version( html, ps) first.