Chapter 2. Random graphs as models of networks

  1. Stefan Bornholdt2 and
  2. Hans Georg Schuster3
  1. Mark E. J. Newman

Published Online: 28 JAN 2005

DOI: 10.1002/3527602755.ch2

Handbook of Graphs and Networks: From the Genome to the Internet

Handbook of Graphs and Networks: From the Genome to the Internet

How to Cite

Newman, M. E. J. (2002) Random graphs as models of networks, in Handbook of Graphs and Networks: From the Genome to the Internet (eds S. Bornholdt and H. G. Schuster), Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim, FRG. doi: 10.1002/3527602755.ch2

Editor Information

  1. 2

    University of Leipzig, Germany

  2. 3

    University of Kiel, Germany

Author Information

  1. Santa Fe Institute, 1399 Hyde Park Road, Santa Fe, NM 87501, USA

Publication History

  1. Published Online: 28 JAN 2005
  2. Published Print: 8 NOV 2002

ISBN Information

Print ISBN: 9783527403363

Online ISBN: 9783527602759

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Keywords:

  • random graphs;
  • networks;
  • probability generating functions;
  • undirected graphs;
  • directed graphs;
  • clustering;
  • resilience;
  • epidemiology;
  • SIR model

Summary

  • Introduction

  • Random graphs with specified degree distributions

  • Probability generating functions

    • Properties of generating functions

    • Examples

  • Properties of undirected graphs

    • Distribution of component sizes

    • Mean component size

    • Above the phase transition

  • Properties of directed graphs

    • Generating functions

    • Results

  • Networks with clustering

  • Models defined on random graphs

    • Network resilience

    • Epidemiology

    • The SIR model

    • Solution of the SIR model

  • Summary

  • References