无标度立体Koch网络的建立及其结构性质研究

Establishment and structure properties of the scale-free Koch network

根据经典Koch曲线的构造,利用四面体作为迭代基元构造了一种立体Koch网络并对其结构性质做了研究,给出了该网络的度分布函数,计算了该网络的团簇系数、平均最短路径长度以及度关联函数.结果表明,所构建的网络是无标度网络,度分布临界指数γ≈3.32;其团簇系数趋向于常数值0.870435;平均路径长度与网络尺寸的对数呈正比关系,说明该网络具有小世界网络特性.另外,计算结果表明knn(k)随k的变化而变化,说明该Koch网络具有一定的度关联性.

According the iterative algorithm of Koch curve,we generate a Koch network by considering tetrahedron as the basic unit of the iteration and investigate its structure properties,such as degree distribution,clustering coefficient,and average path length,degree correlation,analytically.The results show that the network is scale-free and the exponent of the degree distribution is γ ≈3.32.The clustering coefficient tends to be 0.870435 in the limit of large iteration and the study of the average path length proves that the network exhibits small world effect.We also find that the generated network is not degree uncorrelated because the function knn（k） is dependent on the degree of site.