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A generalized approach to complex networks

  • Networks
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The European Physical Journal B - Condensed Matter and Complex Systems Aims and scope Submit manuscript

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.

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References

  • R. Albert, A.L. Barabási, Rev. Mod. Phys. 74, 47 (2002)

    Article  ADS  MathSciNet  Google Scholar 

  • S.N. Dorogovtsev, J.F.F. Mendes, Adv. Phys. 51, 1079 (2002)

    Article  ADS  Google Scholar 

  • S.N. Dorogovtsev, J.F.F. Mendes, Evolution of Networks, From Biological Nets to Internet and WWW (Oxford University Press, 2003)

  • M.E.J. Newman, SIAM Rev. 45, 167 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  • J. Serra, Image Analysis and Mathematical Morphology (Academic Press, 1984)

  • L. Vincent, Signal Proc. 16, 365 (1989)

    Article  MathSciNet  Google Scholar 

  • H.J.A.M. Heijmans, P. Nacken, A. Toet, L. Vincent, J. Vis. Comm. Image Repr. 3, 24 (1992)

    Article  Google Scholar 

  • L. da F. Costa, R.M.C. Jr, Shape Analysis and Classification: Theory and Practice (CRC Press, Boca Raton, 2001)

  • M. Faloutsos, P. Faloutsos, C. Faloutsos, SIAM Rev. 45, 167 (1999)

    Google Scholar 

  • C. Faloutsos, P. Faloutsos, M. Faloutsos, Comp. Comm. Rev. 29, 251 (1999)

    Article  Google Scholar 

  • M.E.J. Newman, e-print arXiv:cond-mat/0111070 (2001)

  • R. Cohen, S. Havlin, S. Mokryn, D. Dolev, T. Kalisky, Y. Shavitt, e-print arXiv:cond-mat/0305582 (2003)

  • L. da F. Costa, Phys. Rev. Lett. 93, 098702 (2004)

    Article  ADS  Google Scholar 

  • L. da F. Costa, e-print arXiv:cond-mat/0412761 (2005)

  • L. da F. Costa, F. Rodrigues, G. Travieso, P.R.V. Boas, e-print arXiv:cond-mat/0505185 (2005)

  • E. Sprinzak, H. Margalit, J. Mol. Biol. 311, 681 (2001)

    Article  Google Scholar 

Download references

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Authors and Affiliations

  1. Institute of Physics of São Carlos, University of São Paulo, Caixa Postal: 369, CEP:, 13560-970, São Carlos, SP, Brazil

    L. da F. Costa & L. E.C. da Rocha

Authors
  1. L. da F. Costa
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  2. L. E.C. da Rocha
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Correspondence to L. da F. Costa.

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Costa, L., da Rocha, L. A generalized approach to complex networks. Eur. Phys. J. B 50, 237–242 (2006). https://doi.org/10.1140/epjb/e2006-00107-0

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  • DOI: https://doi.org/10.1140/epjb/e2006-00107-0

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