基于节点标号的Koch网络结构性质研究

针对正多边形Koch分形岛所映射成的Koch网络,根据节点接入网络的时间和位置信息给节点标号。在节点标号的基础上,研究网络的最短路由及计算最短路径长度;并分析网络的主要结构性质,如节点的度、度分布和累积度分布函数,以及网络的聚类系数、平均最短路径长度、度关联函数和介数中心性,得出结构性质的解析解。结果表明,所构建的Koch网络是无标度和小世界的;其聚类系数趋向于比较大的常数值;平均路径长度与网络节点数的对数呈正比关系,度相关函数、点介数和边介数都随节点度的变化而指数变化。

The Structural Properties of Koch Networks Based on Node Labels

T he Koch Fractal Island ,w hich is starting from a regular polygon ,is mapped to com‐plex evolving Koch networks .The informative labels are given to nodes ,the labels are based on the time and location when nodes are accessing to Koch networks .By the advantages of the in‐formative labels ,we get the exact solution of main structural properties of Koch networks ,inclu‐ding degree distribution and cumulative degree distribution function ,as well as the clustering co‐efficient ,average shortest path length and the correlation function of degree ,betweenness cen‐trality and the shortest path routing and length .The results show that ,Koch network is a scale‐free and small‐world network ;its clustering coefficient tends to relatively large constant ;average shortest path length is proportional to the logarithm of the size of networks ;degree correlation function is exponential function relationship with node's degree .