Advertisement

Scale-free homophilic network

  • Maurício L. de AlmeidaEmail author
  • Gabriel A. MendesEmail author
  • G. Madras Viswanathan
  • Luciano R. da Silva
Regular Article

Abstract

An important aspect governing the growth of complex networks is homophily, which is defined as the tendency of sites to link with others which are similar to themselves. Here, we modify the preferential attachment from Barabási-Albert model by including a homophilic term. Comparisons are made with the Barabási-Albert model, fitness model and our present model considering its topological properties: degree distribution, time dependence of the connectivity, shortest path length and clustering coefficient. We verify the existence of a region where the characteristics of sites play an important role in the rate of gaining links as well as in the number of links between sites with similar and dissimilar characteristics.

Keywords

Statistical and Nonlinear Physics 

References

  1. 1.
    D.J. Watts, Small Worlds: The Dynamics of networks between Order and Randomness (Princeton University Press, Princeton, 2003)Google Scholar
  2. 2.
    A.-L. Barabási, Linked: The New Science of Networks (Perseus Books Group, Cambridge, 2002)Google Scholar
  3. 3.
    S. Dorogovtsev, J.F.F. Mendes, Evolution of Networks: From Biological Nets to the Internet and WWW (Oxford University Press, Oxford, 2003)Google Scholar
  4. 4.
    G.A. Mendes, L.R. da Silva, H.J. Herrmann, Physica A 391, 362 (2012)ADSCrossRefGoogle Scholar
  5. 5.
    P.G. Lind, H.J. Herrmann, J.S. Andrade Jr., L.R. da Silva, Europhys. Lett. 78, 68005 (2007)ADSCrossRefGoogle Scholar
  6. 6.
    P.G. Lind, L.R. da Silva, J.S. Andrade Jr., H.J. Herrmann, Phys. Rev. E 76, 036117 (2007)ADSCrossRefGoogle Scholar
  7. 7.
    G.L. Mamede, N.A.M. Araújo, C.M. Schneider, J.C. de Araújo, H.J. Herrmann, Proc. Natl. Acad. Sci. USA 109, 7191 (2012)ADSCrossRefGoogle Scholar
  8. 8.
    D.J. Watts, S.H. Strogatz, Nature 393, 440 (1998)ADSCrossRefGoogle Scholar
  9. 9.
    L.A.N. Amaral, A. Scala, M. Barthélemy, H.E. Stanley, Proc. Natl. Acad. Sci. USA 97, 509 (2000)CrossRefGoogle Scholar
  10. 10.
    C.M. Schneider, A.A. Moreira, J.S. Andrade Jr., S. Havlin, H.J. Herrmann, Proc. Natl. Acad. Sci. USA 108, 3838 (2011)ADSCrossRefGoogle Scholar
  11. 11.
    C.M. Schneider, N.A.M. Araújo, S. Havlin, H.J. Herrmann, arXiv:1106.3234v1 [cond-mat-stat-mech] (2011)Google Scholar
  12. 12.
    R.F.S. Andrade, J.S. Andrade Jr., H.J. Herrmann, Phys. Rev. E 79, 036105 (2009)ADSCrossRefGoogle Scholar
  13. 13.
    N.A.M. Araújo, R.F.S. Andrade, H.J. Herrmann, Phys. Rev. E 82, 046109 (2010)MathSciNetADSCrossRefGoogle Scholar
  14. 14.
    V.H.P. Louzada, N.A.M. Araújo, J.S. Andrade Jr., H.J. Herrmann, Sci. Rep. 2, 658 (2012)CrossRefGoogle Scholar
  15. 15.
    S. Aral, L. Muchnik, A. Sundararajan, Proc. Natl. Acad. Sci. USA 106, 21544 (2009)ADSCrossRefGoogle Scholar
  16. 16.
    N.N. Chung, L.Y. Chew, J. Zhou, C.H. Lai, Europhys. Lett. 98, 58004 (2012)ADSCrossRefGoogle Scholar
  17. 17.
    A.-L. Barabási, R. Albert, Science 286, 509 (1999)MathSciNetADSCrossRefGoogle Scholar
  18. 18.
    L. da F. Costa, F.A. Rodrigues, G. Travieso, P.R. Villas Boas, Adv. Phys. 56, 167 (2007)ADSCrossRefGoogle Scholar
  19. 19.
    G. Bianconi, A.-L. Barabási, Europhys. Lett. 54, 036112 (2001)Google Scholar
  20. 20.
    G. Caldarelli, A. Capocci, P. De Los Rios, M.A. Munoz, Phys. Rev. Lett. 89, 258702 (2002)ADSCrossRefGoogle Scholar
  21. 21.
    G. Bianconi, P. Pin, M. Marsili, Proc. Natl. Acad. Sci. USA 106, 11433 (2009)ADSCrossRefGoogle Scholar
  22. 22.
    R. Albert, A.-L. Barabási, Rev. Mod. Phys. 74, 47 (2002)ADSzbMATHCrossRefGoogle Scholar
  23. 23.
    G.A. Mendes, L.R. da Silva, Braz. J. Phys. 74, 47 (2002)Google Scholar
  24. 24.
    L. Ferretti, M. Cortelezzi, Phys. Rev. E 84, 016103 (2011)ADSCrossRefGoogle Scholar
  25. 25.
    L. Ferretti, M. Cortelezzi, B. Yang, G. Marmorini, G. Bianconi, Phys. Rev. E 85, 066110 (2012)ADSCrossRefGoogle Scholar
  26. 26.
    W.N.H.C. Shrum Jr., S.M.D. Hunter, Sociol. Educ. 61, 227 (1988)CrossRefGoogle Scholar
  27. 27.
    S.H. Yook, Z.N. Oltvai, A.-L Barabási, Proteomics 4, 928 (2004)CrossRefGoogle Scholar
  28. 28.
    J. Park, A.-L. Barabási, Proc. Natl. Acad. Sci. USA 104, 17916 (2007)ADSCrossRefGoogle Scholar
  29. 29.
    M.E.J. Newman, Phys. Rev. Lett. 89, 208701 (2002)ADSCrossRefGoogle Scholar
  30. 30.
    M.E.J. Newman, J. Park, Phys. Rev. E 68, 036122 (2003)ADSCrossRefGoogle Scholar
  31. 31.
    M. McPherson, L. Smith-Lovin, J.M. Cook, Annu. Rev. Soc. 27, 415 (2001)CrossRefGoogle Scholar
  32. 32.
    S. Cuenda, J.A. Crespo, Europhys. Lett. 95, 38002 (2011)ADSCrossRefGoogle Scholar
  33. 33.
    R.D. Alba, J. Math. Soc. 3, 113 (1973)MathSciNetzbMATHCrossRefGoogle Scholar
  34. 34.
    S.B. Seidman, Social Networks 5, 97 (1983)MathSciNetCrossRefGoogle Scholar
  35. 35.
    L.D. Sailer, S.J.C. Gaulin, Am. Anthropol. 86, 41 (1984)CrossRefGoogle Scholar
  36. 36.
    S.P. Borgatti, M.G. Everett, P.R. Shirey, Social Networks 12, 337 (1990)MathSciNetCrossRefGoogle Scholar
  37. 37.
    D.R. White, F. Haray, Sociological Methodology 31, 305 (2001)CrossRefGoogle Scholar
  38. 38.
    N.A. Christakis, J.H. Fowler, N. Engl. J. Med. 357, 370 (2007)CrossRefGoogle Scholar
  39. 39.
    M.E.J. Newman, G.T. Parkema, Monte Carlo Methods in Statistical Physics (Oxford University Press, Oxford, 1999)Google Scholar
  40. 40.
    J.S. Andrade Jr., H.J. Herrmann, R.F.S. Andrade, L.R. da Silva, Phys. Rev. Lett. 94, 018702 (2005)ADSCrossRefGoogle Scholar
  41. 41.
    F. Liljeros, C.R. Edling, L.A.N. Amaral, H.E. Stanley, Y. Aberg, Nature 411, 907 (2001)ADSCrossRefGoogle Scholar
  42. 42.
    M.E.J. Newman, Phys. Rev. E 64, 016131 (2001)ADSCrossRefGoogle Scholar
  43. 43.
    P. Holme, B.J. Kim, Phys. Rev. E 65, 026107 (2002)ADSCrossRefGoogle Scholar
  44. 44.
    D.J.B. Soares, C. Tsallis, A.M. Mariz, L.R. da Silva, Europhys. Lett. 70, 70 (2005)MathSciNetADSCrossRefGoogle Scholar
  45. 45.
    R. Pastor-Satorras, A. Vázquez, A. Vespignani, Phys. Rev. Lett. 87, 258701 (2001)ADSCrossRefGoogle Scholar
  46. 46.
    S.N. Dorogovtsev, Phys. Rev. E 69, 027104 (2004)ADSCrossRefGoogle Scholar
  47. 47.
    M. Catanzaro, M. Boguñá, R. Pastor-Satorras, Phys. Rev. E 71, 027103 (2004)ADSCrossRefGoogle Scholar

Copyright information

© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.Departamento de Física Teórica e ExperimentalUniversidade Federal do Rio Grande do NorteNatal-RNBrazil
  2. 2.Departamento de FísicaUniversidade Federal do CearáFortaleza-CEBrazil
  3. 3.Instituto de FísicaUniversidade Federal de AlagoasMaceió-ALBrazil

Personalised recommendations