Chapter 4. Structural properties of scale-free networks

  1. Stefan Bornholdt3 and
  2. Hans Georg Schuster4
  1. Reuven Cohen1,
  2. Shlomo Havlin1 and
  3. Daniel ben-Avraham2

Published Online: 28 JAN 2005

DOI: 10.1002/3527602755.ch4

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

Cohen, R., Havlin, S. and ben-Avraham, D. (2002) Structural properties of scale-free 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.ch4

Editor Information

  1. 3

    University of Leipzig, Germany

  2. 4

    University of Kiel, Germany

Author Information

  1. 1

    Minerva Center and Department of Physics, Bar-Ilan University, Ramat-Gan, Israel

  2. 2

    Physics Department and Center for Statistical Physics (CISP), Clarkson University, Potsdam, NY 13699-5820, 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:

  • scale-free networks;
  • structural properties;
  • ultra-small worlds;
  • percolation;
  • directed networks;
  • immunization strategies

Summary

  • Introduction

    • Random graphs

    • Scale-free networks

  • Small and Ultra-small worlds

    • Diameter of scale-free networks

    • Minimal graphs and lower bound

    • The general case of random scale-free networks

  • Percolation

    • Random breakdown

    • Percolation critical threshold

    • Generating functions

    • Intentional attack

    • Critical exponents

    • Fractal dimension

  • Percolation in directed networks

    • Threshold

    • Critical exponents

  • Efficient immunization strategies

    • Acquaintance immunization

  • Summary and outlook

  • References