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Complex Networks from Evolutionary Preferential Attachment

  • Julia Poncela Casasnovas
Chapter
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Part of the Springer Theses book series (Springer Theses)

Abstract

In this chapter we analyze the growth and formation of complex networks by coupling the network formation rules to the dynamical states of the elements of the system. As we have already mentioned, some mechanisms have been proposed for constructing complex scale-free networks similar to those observed in natural, social and technological systems from purely topological arguments (for instance, using a preferential attachment rule or any other rule available in the literature). As those works do not include information on the specific function or origin of the network, it is very difficult to discuss the origin of the observed networks on the basis of those models, hence motivating the question we are going to address. The fact that the existing approaches consider separately the two directions of the feedback loop between the function and form of a complex system demands for a new mechanism where the network grows coupled to the dynamical features of its components. Our aim here is to introduce for the first time an attempt in this direction, by linking the growth of the network to the dynamics taking place among its nodes.

Keywords

Evolutionary Dynamic Degree Distribution Cluster Coefficient Preferential Attachment Degree Correlation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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References

  1. 1.
    M. Newman, SIAM Review 45, 167 (2003).Google Scholar
  2. 2.
    S. Boccaletti, V. Latora, Y. Moreno, M. Chavez, and D. Hwang, Phys. Rep. 424, 175 (2006).Google Scholar
  3. 3.
    G. Bianconi and A. L. Barabási, Europhys. Lett. 54, 436 (2001).Google Scholar
  4. 4.
    G. Caldarelli, A. Capocci, P. D. L. Rios, and M. A. M. noz, Phys. Rev. Lett. 89, 258702 (2002).Google Scholar
  5. 5.
    A. Rapoport and A. M. Chammah, Prisoner’s Dilemma. (Univ. of Michigan Press, Ann Arbor, 1965).Google Scholar
  6. 6.
    K. Lindgren and M. Nordahl, Physica D 75, 292 (1994).Google Scholar
  7. 7.
    M. A. Nowak and R. M. May, Nature 359, 826 (1992).Google Scholar
  8. 8.
    F. C. Santos and J. M. Pacheco, Phys. Rev. Lett. 95, 098104 (2005).Google Scholar
  9. 9.
    H. Gintis, Game theory evolving. (Princeton University Press, Princeton, NJ, 2000).Google Scholar
  10. 10.
    C. Hauert and M. Doebeli, Nature 428, 643 (2004).Google Scholar
  11. 11.
    F. C. Santos, F. J. Rodrigues, and J. M. Pacheco, Proc. Biol. Sci. 273, 51 (2006).Google Scholar
  12. 12.
    J. Hofbauer and K. Sigmund, Evolutionary games and population dy- namics. (Cambridge University Press, Cambridge, UK, 1998).Google Scholar
  13. 13.
    J. Hofbauer and K. Sigmund, Bull. Am. Math. Soc. 40, 479 (2003).Google Scholar
  14. 14.
    J. Gómez-Gardeñes, M. Campillo, L. M. Florí­a, and Y. Moreno, Phys. Rev. Lett. 98, 108103 (2007).Google Scholar
  15. 15.
    M. Nowak, A. Sasaki, C. Taylor, and D. Fudenberg, Nature 428, 646 (2004).Google Scholar
  16. 16.
    M. Nowak, Science 314, 1560 (2006).Google Scholar
  17. 17.
    E. Lieberman, C. Hauert, and M. A. Nowak, Nature 433, 312 (2005).Google Scholar
  18. 18.
    A. Barabási and R. Albert, Science 286, 509 (1999).Google Scholar
  19. 19.
    F. C. Santos and J. M. Pacheco, J. Evol. Biol. 19, 726 (2006).Google Scholar
  20. 20.
    P. Erdos and A. Renyi, Publicationes Mathematicae Debrecen 6, 290 (1959).Google Scholar
  21. 21.
    F. C. Santos, J. M. Pacheco, and T. Lenaerts, Proc. Natl. Acad. Sci. USA 103, 3490 (2006).Google Scholar
  22. 22.
    S. Assenza, J. Gómez-Gardeñes, and V. Latora, Phys. Rev. E 78, 017101 (2008).Google Scholar
  23. 23.
    A. Pusch, S. Weber, and M. Porto, Phys. Rev. E 77, 036120 (2008).Google Scholar
  24. 24.
    L. M. Florí­a, C. Gracia-Lázaro, J. Gómez-Gardeñes, and Y. Moreno, Phys. Rev. E 79, 026106 (2009).Google Scholar
  25. 25.
    R. Axelrod, The complexity of cooperation: agent-based models of com- petition and collaboration. (Princeton University Press., Princeton, NJ, 1997).Google Scholar
  26. 26.
    M. Nowak, Evolutionary dynamics: exploring the equations of life. (Harvard University Press., Cambridge, MA, 2006).Google Scholar
  27. 27.
    M. Nowak and K. Sigmund, Games on Grids, in: The Geometry of Ecological Interactions. (Cambridge University Press, Cambridge, UK, 2000).Google Scholar
  28. 28.
    R. Axelrod and W. Hamilton, Science 211, 1390 (1981).Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Julia Poncela Casasnovas
    • 1
  1. 1.University of ZaragozaZaragozaSpain

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