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Title: Two-dimensional small-world networks: Navigation with local information

Abstract

A navigation process is studied on a variant of the Watts-Strogatz small-world network model embedded on a square lattice. With probability p, each vertex sends out a long-range link, and the probability of the other end of this link falling on a vertex at lattice distance r away decays as r{sup -{alpha}}. Vertices on the network have knowledge of only their nearest neighbors. In a navigation process, messages are forwarded to a designated target. For {alpha}<3 and {alpha}{ne}2, a scaling relation is found between the average actual path length and pL, where L is the average length of the additional long range links. Given pL>1, a dynamic small world effect is observed, and the behavior of the scaling function at large enough pL is obtained. At {alpha}=2 and 3, this kind of scaling breaks down, and different functions of the average actual path length are obtained. For {alpha}>3, the average actual path length is nearly linear with network size.

Authors:
; ;  [1];  [2];  [3]
  1. Department of Physics, Beijing Normal University, Beijing, 100875 (China) and Department of Physics, JiangXi Normal University, Nanchang 330027 (China)
  2. (China)
  3. (World Laboratory), Box 8730, Beijing 100080, China, and Department of Physics, Beijing Normal University, Beijing, 100875 (China)
Publication Date:
OSTI Identifier:
21069770
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics; Journal Volume: 73; Journal Issue: 5; Other Information: DOI: 10.1103/PhysRevE.73.056111; (c) 2006 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND TECHNOLOGY; 60 APPLIED LIFE SCIENCES; LENGTH; PROBABILITY; RANDOMNESS; SCALING LAWS; TWO-DIMENSIONAL CALCULATIONS

Citation Formats

Chen Jianzhen, Liu Wei, Zhu Jianyang, Department of Physics, Beijing Normal University, Beijing, 100875, and CCAST. Two-dimensional small-world networks: Navigation with local information. United States: N. p., 2006. Web. doi:10.1103/PHYSREVE.73.056111.
Chen Jianzhen, Liu Wei, Zhu Jianyang, Department of Physics, Beijing Normal University, Beijing, 100875, & CCAST. Two-dimensional small-world networks: Navigation with local information. United States. doi:10.1103/PHYSREVE.73.056111.
Chen Jianzhen, Liu Wei, Zhu Jianyang, Department of Physics, Beijing Normal University, Beijing, 100875, and CCAST. Mon . "Two-dimensional small-world networks: Navigation with local information". United States. doi:10.1103/PHYSREVE.73.056111.
@article{osti_21069770,
title = {Two-dimensional small-world networks: Navigation with local information},
author = {Chen Jianzhen and Liu Wei and Zhu Jianyang and Department of Physics, Beijing Normal University, Beijing, 100875 and CCAST},
abstractNote = {A navigation process is studied on a variant of the Watts-Strogatz small-world network model embedded on a square lattice. With probability p, each vertex sends out a long-range link, and the probability of the other end of this link falling on a vertex at lattice distance r away decays as r{sup -{alpha}}. Vertices on the network have knowledge of only their nearest neighbors. In a navigation process, messages are forwarded to a designated target. For {alpha}<3 and {alpha}{ne}2, a scaling relation is found between the average actual path length and pL, where L is the average length of the additional long range links. Given pL>1, a dynamic small world effect is observed, and the behavior of the scaling function at large enough pL is obtained. At {alpha}=2 and 3, this kind of scaling breaks down, and different functions of the average actual path length are obtained. For {alpha}>3, the average actual path length is nearly linear with network size.},
doi = {10.1103/PHYSREVE.73.056111},
journal = {Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics},
number = 5,
volume = 73,
place = {United States},
year = {Mon May 15 00:00:00 EDT 2006},
month = {Mon May 15 00:00:00 EDT 2006}
}