从统计物理学看复杂网络研究

从统计物理学来看，网络是一个包含了大量个体及个体之间相互作用的系统。本文从统计物理学的角度整理与总结了复杂网络目前的主要研究结果，并对将来的研究工作做了一个展望。文章把网络分为三个层次——无向网络、有向网络与加权网络，对不同网络的静态几何量研究的现状分别做了综述，并结合网络机制模型设计与评价的需要，提出了新的有待研究的静态几何量；对网络机制模型做了总结与分析，提出了有待解决的关于双向幂律网络的机制模型的问题；部分地概括了网络演化性质，网络的结构稳定性以及网络上的动力学模型的研究。然后，以我们目前正在进行的两个方面的工作—科学家网络和产品生产关系网络一为例，粗略地介绍了网络研究在一些实际问题中的应用。最后，作为一个简单的补充和索引，我们整理了复杂网络研究中部分常用的解析与数值计算的方法。

COMPLEX NETWORKS IN STATISTICAL PHYSICS

From the point view of Statistical Physics, Networks are general many-body systems including all kinds of relations on physical and non-physical interactions. In this article, the authors review most of the main results and organize them by traditional logic of Statistical Physics. An outline 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 waiting for our more attention. Development of networks is related closely with the mechanism model. Some of the works in this aspect are put 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 and 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.