Skip to main content

Preferential attachment with partial information

Abstract

We propose a preferential attachment model for network growth where new entering nodes have a partial information about the state of the network. Our main result is that the presence of bounded information modifies the degree distribution by introducing an exponential tail, while it preserves a power law behaviour over a finite small range of degrees. On the other hand, unbounded information is sufficient to let the network grow as in the standard Barabási-Albert model. Surprisingly, the latter feature holds true also when the fraction of known nodes goes asymptotically to zero. Analytical results are compared to direct simulations.

This is a preview of subscription content, access via your institution.

References

  1. P. Erdős, A. Rényi, Publicationes Mathematicae 6, 290297 (1959)

    Google Scholar 

  2. P. Erdős, A. Rényi, Publications of the Mathematical Institute of the Hungarian Academy of Sciences 5, 1761 (1960)

    Google Scholar 

  3. A. Rapoport, Bull. Math. Biol. 19, 257 (1957)

    MathSciNet  Google Scholar 

  4. M. Newman, A.-L. Barabási, D.J. Watts, The Structure and Dynamics of Networks (Princeton University Press, 2006)

  5. D.J. Watts, S.H. Strogatz, Nature 393, 440 (1998)

    ADS  Article  Google Scholar 

  6. A.-L. Barabási, R. Albert, Science 286, 509 (1999)

    ADS  Article  MathSciNet  Google Scholar 

  7. M. Faloutsos, P. Faloutsos, C. Faloutsos, Comput. Commun. Rev. 29, 251263 (1999)

    Article  Google Scholar 

  8. S. Fortunato, Phys. Rep. 486, 174 (2010)

    Article  MathSciNet  Google Scholar 

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

    ADS  Article  MathSciNet  MATH  Google Scholar 

  10. M.P.H. Stumpf, M.A. Porter, Science 335, 665 (2012)

    ADS  Article  MathSciNet  Google Scholar 

  11. K.B. Hajra, P. Sen, Phys. Rev. E 70, 056103 (2004)

    ADS  Article  Google Scholar 

  12. R. Lambiotte, J. Stat. Mech. 2007, P02020 (2007)

    Google Scholar 

  13. M. Barthelemy, Phys. Rep. 499, 1 (2011)

    ADS  Article  MathSciNet  Google Scholar 

  14. R. Lambiotte et al., Physica A 387, 5317 (2008)

    ADS  Article  MathSciNet  Google Scholar 

  15. J.M. McPherson, L. Smith-Lovin, J.M. Cook, Annu. Rev. Sociol. 27, 415 (2001)

    Article  Google Scholar 

  16. A. Clauset, C.R. Shalizi, M.E.J. Newman, SIAM Rev. 51, 661 (2009)

    ADS  Article  MathSciNet  MATH  Google Scholar 

  17. A. Vázquez, Phys. Rev. E 67, 056104 (2003)

    ADS  Article  Google Scholar 

  18. S. Valverde, R.V. Solé, Europhys. Lett. 72, 858 (2005)

    ADS  Article  Google Scholar 

  19. I. Ispolatov, P.L. Krapivsky, A. Yuryev, Phys. Rev. E 71, 061911 (2005)

    ADS  Article  Google Scholar 

  20. T.S. Evans, J. Saramäki, Phys. Rev. E 72, 26138 (2005)

    ADS  Article  Google Scholar 

  21. S. Fortunato, A. Flammini, F. Menczer, Phys. Rev. Lett. 96, 218701 (2006)

    ADS  Article  Google Scholar 

  22. R.M. D’Souza, P.L. Krapivsky, C. Moore, Eur. Phys. J. B 59, 535 (2007)

    ADS  Article  MathSciNet  MATH  Google Scholar 

  23. H. Štefančić, V. Zlatić, Phys. Rev. E 72, 036105 (2005)

    ADS  Article  Google Scholar 

  24. S. Mossa et al., Phys. Rev. Lett. 88, 138701 (2002)

    ADS  Article  Google Scholar 

  25. H. Štefančić, V. Zlatić, Physica A 350, 657 (2005)

    ADS  Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Renaud Lambiotte.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Carletti, T., Gargiulo, F. & Lambiotte, R. Preferential attachment with partial information. Eur. Phys. J. B 88, 18 (2015). https://doi.org/10.1140/epjb/e2014-50595-0

Download citation

  • Received:

  • Revised:

  • Published:

  • DOI: https://doi.org/10.1140/epjb/e2014-50595-0

Keywords

  • Statistical and Nonlinear Physics