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Optimization in Complex Networks


  • Ramon Ferrer i Cancho
  • Ricard V. Solé


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.

Suggested Citation

  • Ramon Ferrer i Cancho & Ricard V. Solé, 2001. "Optimization in Complex Networks," Working Papers 01-11-068, Santa Fe Institute.
  • Handle: RePEc:wop:safiwp:01-11-068

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    References listed on IDEAS

    1. Stanley, E.A. & Ashlock, Daniel & Tesfatsion, Leigh, 1994. "Iterated Prisoner's Dilemma with Choice and Refusal of Partners," Staff General Research Papers Archive 11180, Iowa State University, Department of Economics.
    2. Dutta Prajit K., 1995. "A Folk Theorem for Stochastic Games," Journal of Economic Theory, Elsevier, vol. 66(1), pages 1-32, June.
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    Complex networks; optimization; scale-free nets; small world; evolution;

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