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Optimization in Complex Networks

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  • Ramon Ferrer i Cancho
  • Ricard V. Solé
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    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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    Bibliographic Info

    Paper provided by Santa Fe Institute in its series Working Papers with number 01-11-068.

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    Date of creation: Nov 2001
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    Handle: RePEc:wop:safiwp:01-11-068

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    Related research

    Keywords: Complex networks; optimization; scale-free nets; small world; evolution;

    This paper has been announced in the following NEP Reports:

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