Self-similarity of complex networks View Full Text


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Article Info

DATE

2005-01

AUTHORS

Chaoming Song, Shlomo Havlin, Hernán A. Makse

ABSTRACT

Complex networks have been studied extensively owing to their relevance to many real systems such as the world-wide web, the Internet, energy landscapes and biological and social networks. A large number of real networks are referred to as 'scale-free' because they show a power-law distribution of the number of links per node. However, it is widely believed that complex networks are not invariant or self-similar under a length-scale transformation. This conclusion originates from the 'small-world' property of these networks, which implies that the number of nodes increases exponentially with the 'diameter' of the network, rather than the power-law relation expected for a self-similar structure. Here we analyse a variety of real complex networks and find that, on the contrary, they consist of self-repeating patterns on all length scales. This result is achieved by the application of a renormalization procedure that coarse-grains the system into boxes containing nodes within a given 'size'. We identify a power-law relation between the number of boxes needed to cover the network and the size of the box, defining a finite self-similar exponent. These fundamental properties help to explain the scale-free nature of complex networks and suggest a common self-organization dynamics. More... »

PAGES

392

References to SciGraph publications

  • 2004-03. Complex networks in THE EUROPEAN PHYSICAL JOURNAL B
  • 1988. Fractals in NONE
  • 1999-09. Internet: Diameter of the World-Wide Web in NATURE
  • 2000-10. The large-scale organization of metabolic networks in NATURE
  • 1998-06. Collective dynamics of ‘small-world’ networks in NATURE
  • 1996. Fractals and Disordered Systems in NONE
  • Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1038/nature03248

    DOI

    http://dx.doi.org/10.1038/nature03248

    DIMENSIONS

    https://app.dimensions.ai/details/publication/pub.1033900087

    PUBMED

    https://www.ncbi.nlm.nih.gov/pubmed/15674285


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