一类作为网络模型的可平面无标度图

摘要

无标度特性普遍存在于大量的实际网络和人造网络中.为了更好地研究这类无标度网络模型的拓扑性质和内在动力学,大量的模型被建立,如随机网络模型和确定性网络模型.鉴于以往确定性模型中的无标度指数都是唯一不变的常数,定义了一类具有广义自相似性的增长网络模型,分析了它的一些拓扑性质:平均度、聚集系数、直径、度分布、最多叶子生成树.得出该模型具有无标度特性和小世界效应,并且可以通过调整相应的参数来获得丰富的无标度指数.%The scale-free feature is popular in amounts of real-life and artificial complex networks.In order to study the topological properties and intrinsic dynamics of this kind of scale-free network model,lots of models are presented, such as random network models and deterministic ones. Considering that the scale-free exponent is an unique constant in those previous deterministic models, a generalized self-similarity growing network model is proposed.Its topological properties,including average degree,clustering coefficient,diameter,degree distribution,maximum-leaf-spanning-tree are analyzed.It shows that this model has scale-free characteristics and small-world effects,and the scale-free exponent can be enriched by adjusting corresponding parameters.