Optimization in Complex Networks

  • Ramon Ferrer i Cancho
  • Ricard V. Solé
Chapter
Part of the Lecture Notes in Physics book series (LNP, volume 625)

Abstract

Many complex systems can be described in terms of networks of interacting units. Recent studies have shown that a wide class of both natural and artificial nets display a surprisingly widespread feature: the presence of highly heterogeneous distributions of links, providing an extraordinary source of robustness against perturbations. Although most theories concerning the origin of these topologies use growing graphs, here we show that a simple optimization process can also account for the observed regularities displayed by most complex nets. Using an evolutionary algorithm involving minimization of link density and average distance, four major types of networks are encountered: (a) sparse exponential-like networks, (b) sparse scale-free networks, (c) star networks and (d) highly dense networks, apparently defining three major phases. These constraints provide a new explanation for scaling of exponent about -3. The evolutionary consequences of these results are outlined.

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Copyright information

© Springer-Verlag Berlin/Heidelberg 2003

Authors and Affiliations

  • Ramon Ferrer i Cancho
    • 1
  • Ricard V. Solé
    • 1
    • 2
  1. 1.ICREA-Complex Systems LabUniversitat Pompeu Fabra (GRIB)BarcelonaSpain
  2. 2.Santa Fe InstituteSanta FeUSA

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