一种星–树结构的确定性的小世界网络

A Star-Tree-Structured Deterministic Small-World Network

摘要: 在过去的的几十年，人们运用各种机制建构了许多不确定性的和确定性的小世界网络。最近，郭世泽等人通过在星图K_1,2上运用一个简单的算法在每个迭代步添加一些边首次形成了一个二叉树结构的确定性的小世界网络。本文通过一个星图K_1,6在每个迭代步连接每个树的各祖父节点和它的四个孙子节点，由此构建一个二叉树结构的新的确定性的小世界网络模型。此外，我们给出了一些拓扑属性的分析结果，它表明构建的模型是小世界网络。

Abstract: In the past dozen years, many probabilistic small-world networks and some deterministic small- world networks have been proposed utilizing various mechanisms. Recently, Guo et al. proposed a deterministic small-world network model by first constructing a binary-tree structure from star K_1,2 by adding some edges in each iteration with a simple mechanism. In this paper, we propose a new deterministic small-world network model by constructing a binary-tree structure from a star K_1,6 and then adding links between each grandfather node and its four grandson nodes for each tree in each iteration. Furthermore, we give the analytic solution to several topological characteristics, which shows that the proposed model is a small-world network.