Chapter 1. Mathematical results on scale-free random graphs

  1. Stefan Bornholdt3 and
  2. Hans Georg Schuster4
  1. Béla Bollobás1,2 and
  2. Oliver M. Riordan2

Published Online: 28 JAN 2005

DOI: 10.1002/3527602755.ch1

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

Bollobás, B. and Riordan, O. M. (2002) Mathematical results on scale-free random graphs, 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.ch1

Editor Information

  1. 3

    University of Leipzig, Germany

  2. 4

    University of Kiel, Germany

Author Information

  1. 1

    Department of Mathematical Sciences, University of Memphis, Memphis TN 38152, USA

  2. 2

    Trinity College, Cambridge CB2 1TQ, UK

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:

  • scale-free random graphs;
  • mathematical results;
  • classical models;
  • Watts-Strogatz ‘small-world’ model;
  • Barabási-Albert model;
  • LCD model;
  • Buckley-Osthus model;
  • copying model;
  • Cooper-Frieze model;
  • robustness

Summary

  • Introduction

  • Classical models of random graphs

  • Results for classical random graphs

  • The Watts-Strogatz ‘small-world’ model

  • Scale-free models

  • The Barabási-Albert model

  • The LCD model and Gm(n)

  • The Buckley-Osthus model

  • The copying model

  • The Cooper-Frieze model

  • Directed scale-free graphs

  • Clustering coefficient and small subgraphs

  • Pairings on [0, 1] and the diameter of the LCD model

  • Robustness and vulnerability

  • The case [0, 1]: plane-oriented recursive trees

  • Conclusion

  • References