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Lectures on Complex Networks$
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Sergey Dorogovtsev

Print publication date: 2010

Print ISBN-13: 9780199548927

Published to Oxford Scholarship Online: May 2010

DOI: 10.1093/acprof:oso/9780199548927.001.0001

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Small and large worlds

Small and large worlds

Chapter:
(p.17) 3 Small and large worlds
Source:
Lectures on Complex Networks
Author(s):

Sergey N. Dorogovtsev

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780199548927.003.0003

This chapter discusses and compares the geometries of small worlds, lattices and fractals. The first measurements of the diameter of the World Wide Web are described. The Watts–Strogatz model of a small-world network and crossover from a lattice to a small world are discussed. The fractal properties of giant connected components near the birth points are described and their fractal dimensions are discussed.

Keywords:   small-world phenomenon, lattices, fractal dimension, average shortest-path length

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