一种星–树结构的确定性的小世界网络
A Star-Tree-Structured Deterministic Small-World Network
DOI: 10.12677/CSA.2014.411038, PDF,    国家自然科学基金支持
作者: 侯鹏锋：青海师范大学数学系，西宁；赵海兴：青海师范大学计算机学院，西宁
关键词: 小世界网络；星–树结构；拓扑属性；Small World Network； Star-Tree-Structure； Topological Characteristics
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K1,2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K1,6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 K1,2 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 K1,6 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.
文章引用：侯鹏锋, 赵海兴. 一种星–树结构的确定性的小世界网络[J]. 计算机科学与应用, 2014, 4(11): 276-281. https://dx.doi.org/10.12677/CSA.2014.411038

参考文献

[1] Guo, S.Z., Lu, Z.M., Kang, G.Y., Chen, Z. and Luo, H. (2012) A tree-structured deterministic small-world network. IEICE Transactions on Information and Systems, E95-D.
[2] Watts, D.J. and Strogatz, S.H. (1998) Collective dy-namics of “small-world” networks. Nature, 393, 440-442.
[3] Newman, M.E.J. and Watts, D.J. (1999) Renormaliza-tion group analysis of the small-world network model. Physics Letters A, 263, 341-346.
[4] Newman, M.E.J. and Watts, D.J. (1999) Scaling and percolation in the small-world network model. Physical Review E, 60, 7332-7342.
[5] Kasturirangan, R. (1999) Multiple scales in small-world network.
[6] Ozik, J., Hunt, B.-R. and Ott, E. (2004) Growing networks with geographical attachment preference: Emergence of small worlds. Physical Review E, 69, Article ID: 026108.
[7] Comellas, F., Ozon, J. and Peters, J.G. (2000) Deterministic small-world communication networks. Information Processing Letters, 76, 83-90.
[8] Boettcher, S., Gongalves, B. and Guclu, H. (2008) Hie-rarchical regular small-world networks. Physics A: Mathematical and Theoretical, 41, Article ID: 252001.
[9] Chandra, A.K. and Dasgupta, S. (2005) A small world network of prime numbers. Physica A, 357, 436-446.
[10] Corso, G. (2004) Families and clustering in a natural numbers network. Physical Review E, 69, Article ID: 036106.
[11] Xiao, W.J. and Parhami, B. (2006) Cayley graphs as models of deterministic small-world networks. Information Pro- cessing Letters, 97, 115-117.