具有老化机制的阿波罗网络模型  

Model of apollonian networks with aging mechanism

作　　者：那日萨[1] 张书超[1] 

机构地区：[1]大连理工大学系统工程研究所,大连116023

出　　处：《系统工程理论与实践》2008年第9期92-97,165,共7页Systems Engineering-Theory & Practice

基　　金：国家自然科学基金(70571007)

摘　　要：提出了一个具有老化机制的阿波罗网络模型.通过数学解析的方法得到了模型演化网络的节点的度分布和集聚系数的表达式,并推理出网络的平均路径长度是以网络规模的对数形式增长,表明了该网络同时具有小世界和无标度特性.通过计算机的模拟计算,得到的仿真结果与解析结果达到了很好的吻合,同时给出了节点的年龄分布,证明节点获得新连接的概率和年龄呈负相关关系,从而说明了本模型比随机阿波罗网络模型更符合现实网络.最后,分析了网络的可平面性及其对现实的理论指导意义.In relation to the problem of Apollonian packing, the ApoUonian network is introduced. It has interesting properties like being scale-free, small-world, space-filling, may help to explain the properties of energy landscapes and can be apphed to porous media, mad networks, electrical systems and the layout of the planar network. For the further research on the Apallonian network, we propase a model of Apollonian Networks with aging mechanism. Using mathematical analysis, we deduce that the degree distribution obeys power-law form, which indicates that the network is pawer-law. Also we obtain the expression of clustering coefficient and prove that the average path length increases in form of logarithm of network size, which indicates that the network is small-world. And then, the simulation results are given out, which agrees with the theoretic calculations. At last, we calculate the distribution of age of nodes, prove that the age of a node negatively correlates to the probability of the node＇ s getting new links, and analyze that the network is a planar network. Therefore, the model proposed in this paper performs better than the model of Random Apallonian Networks and is more effective to the practice of layout of planar networks, such as printed circuits.

关 键 词：阿波罗网络 老化 小世界网络 无标度网络 复杂网络 

分 类 号：N94[自然科学总论—系统科学] O173[理学—数学]