Chapter 16. Graph theory and the evolution of autocatalytic networks

  1. Stefan Bornholdt3 and
  2. Hans Georg Schuster4
  1. Sanjay Jain1,2 and
  2. Sandeep Krishna2

Published Online: 28 JAN 2005

DOI: 10.1002/3527602755.ch16

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

Jain, S. and Krishna, S. (2002) Graph theory and the evolution of autocatalytic 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.ch16

Editor Information

  1. 3

    University of Leipzig, Germany

  2. 4

    University of Kiel, Germany

Author Information

  1. 1

    Department of Physics and Astrophysics, University of Delhi, Delhi 110007, India

  2. 2

    Centre for Theoretical Studies, Indian Institute of Science, Bangalore 560 012, India

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:

  • graph theory;
  • autocatalytic networks;
  • graph dynamics;
  • self-organization;
  • catastrophes;
  • recoveries;
  • organized phase

Summary

  • Introduction

  • Graph theory and autocatalytic sets

    • Directed graphs and their adjacency matrices

    • Autocatalytic sets

  • A dynamical system on a fixed graph

    • Attractors of equation (16.1)

  • Graph dynamics

  • Self Organization

    • The random phase

    • The growth phase

    • The organized phase

  • Catastrophes and recoveries in the organized phase

    • Catastrophes, core-shifts and a classification of proximate causes

    • Recoveries

    • Correlation between graph theoretic nature of perturbation and its short and long term impact

  • Concluding remarks

  • References