Chapter

Classical random graphs

Sergey N. Dorogovtsev

in Lectures on Complex Networks

Published in print February 2010 | ISBN: 9780199548927
Published online May 2010 | e-ISBN: 9780191720574 | DOI: http://dx.doi.org/10.1093/acprof:oso/9780199548927.003.0002

Series: Oxford Master Series in Physics

Classical random graphs

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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

Chapter.  4618 words.  Illustrated.

Subjects: Mathematical and Statistical Physics

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