复杂网络研究的经验结果

The Results of Empirical Research on Complex Network

网络研究已经成为揭示自然界及人类社会各种复杂性系统结构及功能的重要手段。尽管组成真实网络的元素非常不同,网络拓扑也有其自身的复杂性,但大量经验结果显示这些截然不同的网络普遍存在着某些共同性质。因此,要更好地揭示复杂网络的基本性质和功能,我们除了对包含大量元素的复杂系统进行统计外还要对各种不同的网络类型进行分析。这篇论文综述了近年网络研究的成果和进展,归纳复杂网络结构的几个基本性质,包括小世界特征、高聚集性以及确定的连接度分布尤其是无标度度分布行为。

The study of networks has become an important means for revealing complex systems and structures of natural world and human society. It has been discovered that many real network systems, while showing different levels of complexity of their own, possess some common structural or topological properties: the small-world effect, the high-clustering, and a well-defined degree distribution,etc, To understand the properties and functionalities of networks, study based on large-scale systems is required. This has become feasible nowadays due to the rapid development of computers and Interdisciplinary Physics. In fact, many statistical physicists have devoted themselve to this field and a great achievement has been made. In this paper, the author first reviews the rapid progress and result in the study of evolving networks, and then points out several important features including the small-world effect, the high-clustering, well-defined, and especially, the scale-free distribution of degrees.