中文摘要：

为扩展复杂网络模型并探讨网络的新特征，研究了随机复杂网络的统计性质．在以两种菱形为结构单元的彭罗斯拼图的基础上，增加顶点的随机连接，其连接概率与顶点的类型有关，由此构造出部分随机的复杂网络．用解析和数值方法计算了网络的主要特征参数．结果表明：度分度、节点间平均距离和网络集群系数与一般随机网络接近，但具体变化规律有所不同．由此可见，准周期复杂网络既有一般网络的共性，也有更为丰富的其他特征．

英文摘要：

In order to extend the models and exploit new features for complex networks, the statistical properties of random complex networks are explored. In the investigation, first, on the basis of the Penrose tiling composed of two kinds of rhombus, random connections of the vertex are added to construct a partially random complex network in which the connecting probability depends on the vertex type. Then, the main characteristic parameters of the network are calculated by using analytical and numerical methods. It is found that the degree distribution, the ave- rage inter-node distance and the cluster coefficient of the partially random complex network are all close to those of general random networks but obey different variation laws, which means that the proposed quasi-periodic complex network possesses not only the common properties of general networks but also abundant specific features.