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Modified Penna bit-string network evolution model for scale-free networks with assortative mixing

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Abstract

Motivated by biological aging dynamics, we introduce a network evolution model for social interaction networks. In order to study the effect of social interactions originating from biological and sociological reasons on the topological properties of networks, we introduce the activitydependent rewiring process. From the numerical simulations, we show that the degree distribution of the obtained networks follows a power-law distribution with an exponentially decaying tail, P(k) ∼ (k + c)γ exp(−k/k 0). The obtained value of γ is in the range 2 < γ š 3, which is consistent with the values for real social networks. Moreover, we also show that the degree-degree correlation of the network is positive, which is a characteristic of social interaction networks. The possible applications of our model to real systems are also discussed.

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References

  1. M. E. J. Newman, Networks: An Introduction (Oxford University Press, Oxford, 2010).

    MATH  Google Scholar 

  2. S-H. Yook, H. Jeong and A-L. Barabási, Proc. Nat. Acad. Sci. 99, 13382 (2002).

    Article  ADS  Google Scholar 

  3. Y. Kim, J-H. Kim and S-H. Yook, Phys. Rev. E 83, 056115 (2011).

    Article  ADS  Google Scholar 

  4. S-H. Yook, Z. Oltvai and A-L. Barabási, Proteomics 4, 928 (2003).

    Article  Google Scholar 

  5. H. Ebel, L-I. Mielsch and S. Bornholdt, Phys. Rev. E 66, 035103(R) (2002).

    ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  7. R. Albert, H. Jeong and A-L. Barabási, Nature 401, 130 (1999).

    Article  ADS  Google Scholar 

  8. M. E. J. Newman, Phys. Rev. E 64, 016131 (2001).

    Article  ADS  Google Scholar 

  9. R. Albert and A-L. Barabási, Rev. Mod. Phys. 74, 47 (2002).

    Article  ADS  MATH  Google Scholar 

  10. A-L. Barabási, R. Albert and H. Jeong, Physica A 272, 173 (1999).

    Article  ADS  Google Scholar 

  11. P. Erdös and A. Rényi, Publ. Math-Debrecen 6, 290 (1959).

    MathSciNet  MATH  Google Scholar 

  12. M. E. J. Newman, Phys. Rev. Lett. 89, 208701 (2002).

    Article  ADS  Google Scholar 

  13. S-H. Yook and H. Meyer-Ortmanns, Phys. Rev. E 72, 045105(R) (2005).

    Article  ADS  Google Scholar 

  14. L. K. Gallos, C. Song, S. Havlin and H. A. Makse, Proc. Nat. Acad. Sci. 104, 7746 (2007).

    Article  ADS  Google Scholar 

  15. C. Li and P. K. Maini, Phys. Rev. E 72, 045102(R) (2005).

    ADS  Google Scholar 

  16. D. Stauffer, S. M. de Oliveira, P. M. C. de Oliveira and J. S. Sá Martins, Biology, Sociology, Geology by Computational Physicists (Elsevier, Amsterdam, 2006).

    MATH  Google Scholar 

  17. T. J. P. Penna, J. Stat. Phys. 78, 1629 (1995).

    Article  ADS  MATH  Google Scholar 

  18. D. Stauffer, Biological Evolution and Statistical Physics, edited by M. Lässig and A. Valleriani (Springer, Berlin-Heidelberg, 2002), p. 258.

    Google Scholar 

  19. B. Gompertz, Philos. T. R. Soc. Lond. 115, 513 (1825).

    Article  Google Scholar 

  20. M. Magdoń-Maksymowicz, A. Z. Maksymowicz and K. Kułakowski, Theor. Biosci. 119, 139 (2000).

    Google Scholar 

  21. H. Jeong, S. P. Mason, A.-L. Barabási and Z. N. Oltvai, Nature 411, 41 (2001).

    Article  ADS  Google Scholar 

  22. A. Vázquez, A. Flammini, A. Maritan and A. Vespignani, ComPlexUs 1, 38 (2003).

    Article  Google Scholar 

  23. V. Colizza, A. Flammini, A. Maritan and A. Vespignani, Physica A 352, 1 (2005).

    Article  ADS  Google Scholar 

  24. R. Pastor-Satorras, A. Vázquez and A. Vespignani, Phys. Rev. Lett. 87, 258701 (2001).

    Article  ADS  Google Scholar 

  25. http://plus.google.com

  26. S. Scellato and C. Mascolo, in 2011 IEEE Conference on Computer Communication Workshops (INFOCOM WKSHPS, 2011), p. 918.

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Correspondence to Soon-Hyung Yook.

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Kim, Y., Choi, W. & Yook, SH. Modified Penna bit-string network evolution model for scale-free networks with assortative mixing. Journal of the Korean Physical Society 60, 621–624 (2012). https://doi.org/10.3938/jkps.60.621

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  • DOI: https://doi.org/10.3938/jkps.60.621

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