A Tree-Structured Deterministic Small-World Network

• Published in: IEICE Transactions on Information and Systems Vol. E95.D; no. 5; pp. 1536 - 1538
• Main Authors: GUO, Shi-Ze, LU, Zhe-Ming, KANG, Guang-Yu, LUO, Hao, CHEN, Zhe
• Format: Journal Article
• Language: English
• Published: Oxford The Institute of Electronics, Information and Communication Engineers 2012; Oxford University Press
• Subjects: Applied sciences; average path length; Business and industry local networks; Clustering; clustering coefficient; Construction; Design. Technologies. Operation analysis. Testing; deterministic small-world models; Electronics; Exact sciences and technology; Exact solutions; Information, signal and communications theory; Integrated circuits; Interconnection network; Links; Networks; Networks and services in france and abroad; Probabilistic methods; Probability theory; Semiconductor electronics. Microelectronics. Optoelectronics. Solid state devices; Signal and communications theory; Signal representation. Spectral analysis; Signal, noise; Telecommunications; Telecommunications and information theory; Teleprocessing networks. Isdn; Topology; tree-structured network; Valuation and optimization of characteristics. Simulation; Interconnection network; Automatic classification; Peer to peer; Probabilistic approach; clustering coefficient; Resource sharing; Tree structure; Signal classification; Local network; Aggregation; Binary tree; Computer network; Deterministic model; Analytical method; deterministic small-world models; Deterministic approach; average path length; tree-structured network
• ISSN: 0916-8532; 1745-1361; 1745-1361
• DOI: 10.1587/transinf.E95.D.1536

Small-world is a common property existing in many real-life social, technological and biological networks. Small-world networks distinguish themselves from others by their high clustering coefficient and short average path length. In the past dozen years, many probabilistic small-world networks and some deterministic small-world networks have been proposed utilizing various mechanisms. In this Letter, we propose a new deterministic small-world network model by first constructing a binary-tree structure and then adding links between each pair of brother nodes and links between each grandfather node and its four grandson nodes. Furthermore, we give the analytic solutions to several topological characteristics, which shows that the proposed model is a small-world network.