论文标题
在一类无层次尺度网络上的某些结构属性的分析
Analyses of Some Structural Properties on a Class of Hierarchical Scale-free Networks
论文作者
论文摘要
层次网络实际上在现实世界中具有许多应用程序。首先，我们提出了一个具有无规模和分形结构的新类层次网络，与传统的分层网络相比，它们是具有三角形的网络。其次，我们研究了某些结构特性的精确结果，以得出小世界效应和无尺度特征。第三，发现构造的网络在平均程度和密度下稀疏。第四，也证明了轮毂节点的度分布，底部节点分别是幂律和指数。最后，我们证明，具有确定值z的聚类系数倾向于在t到一定数的情况下稳定下的下限，而g_ {t}^{z}的平均距离与lnn_ {t}的值以及lnn_ {t}的值具有越来越多的关系。
Hierarchical networks actually have many applications in the real world. Firstly, we propose a new class of hierarchical networks with scale-free and fractal structure, which are the networks with triangles compared to traditional hierarchical networks. Secondly, we study the precise results of some structural properties to derive small-world effect and scale-free feature. Thirdly, it is found that the constructed network is sparse through the average degree and density. Fourthly, it is also demonstrated the degree distributions of hub nodes and the bottom nodes are the power law and exponential, respectively. Finally, we prove that clustering coefficient with a definite value z tends to stabilize at a lower bound as t iterates to a certain number, and the average distance of G_{t}^{z} has a increasing relationship along with the value of lnN_{t}.
