中文摘要：

复杂网络模型的研究主要集中在ER网络模型、小世界网络模型和无标度网络模型,其中ER网络模型是最经典的复杂网络模型之一。文章研究了节点数固定情况下的ER网络模型,根据网络内部边的动态演化特点,将节点数固定的网络模型进行了细分,给出了模型的生成算法,并模拟了算法生成的随机网络的平均路径长度和聚类系数。仿真结果表明,节点数固定的ER网络具有小世界特性,出现这种小世界特性的主要原因是由于网络内部边的异质性,而与网络的节点数变化没有必然联系。

英文摘要：

The complex network have three kinds of major model-ER model,small-world network model and the scale-free network model,and the ER model is the most classical one.In this paper,we mainly study the ER network model based on fixed nodes.According to the dynamic evolution characteristic of the ER network,sorting the ER networks into two different kinds,and the model production algorithm is given.According to two different modes of connective edge,average shortest path lengths and clustering coefficients are compared.It has been indicated that ER networks with fixed nodes have small-world characteristics,and the primary reason of phenomena existing is different methods of connective edge,but not node＇s number.