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A generalized approach to complex networks

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  • L. da F. Costa
  • L. E.C. da Rocha

Abstract

This work describes how the formalization of complex network concepts in terms of discrete mathematics, especially mathematical morphology, allows a series of generalizations and important results ranging from new measurements of the network topology to new network growth models. First, the concepts of node degree and clustering coefficient are extended in order to characterize not only specific nodes, but any generic subnetwork. Second, the consideration of distance transform and rings are used to further extend those concepts in order to obtain a signature, instead of a single scalar measurement, ranging from the single node to whole graph scales. The enhanced discriminative potential of such extended measurements is illustrated with respect to the identification of correspondence between nodes in two complex networks, namely a protein-protein interaction network and a perturbed version of it. Copyright EDP Sciences/Società Italiana di Fisica/Springer-Verlag 2006

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  • L. da F. Costa & L. E.C. da Rocha, 2006. "A generalized approach to complex networks," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 50(1), pages 237-242, March.
    • Handle: RePEc:spr:eurphb:v:50:y:2006:i:1:p:237-242
    DOI: 10.1140/epjb/e2006-00107-0
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    References listed on IDEAS

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    1. Dorogovtsev, S.N. & Mendes, J.F.F., 2003. "Evolution of Networks: From Biological Nets to the Internet and WWW," OUP Catalogue, Oxford University Press, number 9780198515906.
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    Cited by:

    1. Costa, Luciano da Fontoura & Rodrigues Tognetti, Marilza A. & Silva, Filipi Nascimento, 2008. "Concentric characterization and classification of complex network nodes: Application to an institutional collaboration network," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(24), pages 6201-6214.

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