节点数固定的复杂网络模型初探

由于随机图模型、小世界模型和无标度模型的结构上存在交叉性，有必要对复杂网络进行新的分类。本文将复杂网络分成两类：节点数固定的复杂网络和节点数变化的复杂网络，且重点研究了前一类网络。首先时节点数固定的网络进行了细分，然后分析了在边的不同连接方式下节点数固定的网络的度分布、平均最短路长度和聚类系数等特征，最后讨论了小世界特性与无标度特性产生的原因。研究表明，节点数固定的网络大多具有小世界特性，小世界特性与无标度特性是从不同的侧面来研究复杂网络的，从而很好地解释了在许多复杂网络这两种特性能够共存的原因。

Discussion about Complex Networks with Invariable Vertex Numbers

The discoveries of many natural and artificial complex networks,like the Internet,World Wide Web and the citation networks,have aroused physical communities' great interest.It is necessary to classify rationally the complex networks because of the intercross on the structure among the random graph models,small-world network and scale-free network models.In this paper,we sort the complex networks into two different kinds.One is the complex networks with invariable vertex numbers,the other is those with increasing vertex numbers.Then the properties of the former kind are studied in detail.According to three different modes of connective edge,degree distributions,average shortest path lengths and clustering coefficients of the first kind are compared.It has been indicated that most networks with invariable vertex numbers have small-world characteristics,and small-world property and scale-free property depict different profiles of evolving networks.It does commendably explain why small-world and scale-free phenomena coexist in many real complex networks.