A Tree-Structured Deterministic Small-World Network

Abstract

SUMMARYSmall-world is a common property existing in many reallife 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. key words: deterministic small-world models, tree-structured network, Interconnection network, average path length, clustering coefficient

Random Walks on Stochastic and Deterministic Small-World Networks

“…Thus, this model is a deterministic small-world network. Another deterministic small-world network proposed by Guo et al [10] focuses on the iteration of a binary-tree structure. At each iteration, after adding two new branches from each node in the last layer as the usual binary-tree structure, we additionally add links between each pair of brother nodes and links between each grandfather node and its four grandson nodes.…”

“…In 2006, Zhang et al presented a deterministic small-world network created by edge iterations [9]. Recently, Guo et al presented a tree-structured deterministic small-world model [10], while Lu and Guo proposed a deterministic small-world model derived from the uniform recursive tree [11]. The most evident advantage provided by deterministic networks is that we can calculate their properties analytically.…”