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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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Classical random graphs

Classical random graphs

Chapter:
(p.9) 2 Classical random graphs
Source:
Lectures on Complex Networks
Author(s):

Sergey N. Dorogovtsev

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780199548927.003.0002

This chapter gives insight into the simplest and most studied random networks: the classical random graphs. The Erdös–Rényi and Gilbert models are described, and some of their properties and characteristics are considered. These characteristics include a Poisson degree distribution, the number of loops and clustering, and average shortest-path length. The statistics of connected components in these random networks and the birth of a giant connected component, are considered.

Keywords:   Erdös–Rényi model, giant connected component, Poisson degree distribution

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