A complementary view on the growth of directory trees


Trees are a special sub-class of networks with unique properties, such as the level distribution which has often been overlooked. We analyse a general tree growth model proposed by Klemm et al. [Phys. Rev. Lett. 95, 128701 (2005)] to explain the growth of user-generated directory structures in computers. The model has a single parameter q which interpolates between preferential attachment and random growth. Our analysis results in three contributions: first, we propose a more efficient estimation method for q based on the degree distribution, which is one specific representation of the model. Next, we introduce the concept of a level distribution and analytically solve the model for this representation. This allows for an alternative and independent measure of q. We argue that, to capture real growth processes, the q estimations from the degree and the level distributions should coincide. Thus, we finally apply both representations to validate the model with synthetically generated tree structures, as well as with collected data of user directories. In the case of real directory structures, we show that q measured from the level distribution are incompatible with q measured from the degree distribution. In contrast to this, we find perfect agreement in the case of simulated data. Thus, we conclude that the model is an incomplete description of the growth of real directory structures as it fails to reproduce the level distribution. This insight can be generalised to point out the importance of the level distribution for modeling tree growth.

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  1. 1.

    G. Caldarelli, Scale-Free Networks (Oxford University Press, 2007)

  2. 2.

    I. Rodríguez-Iturbe, A. Rinaldo, Fractal River Basins: Chance and Self-Organization (Cambridge University Press, 1997)

  3. 3.

    M. Zamir, J. Theor. Biol. 197, 517 (1999)

    Article  Google Scholar 

  4. 4.

    E. Weibel, American Journal of Physiology-Lung Cellular and Molecular Physiology 261, 361 (1991)

    Google Scholar 

  5. 5.

    J.R. Banavar, A. Maritan, A. Rinaldo, Nature 399, 130 (1999)

    Article  ADS  Google Scholar 

  6. 6.

    P. Prusinkiewicz, A. Lindenmayer, The algorithmic beauty of plants (Springer-Verlag, Inc., New York, NY, USA, 1990)

    Google Scholar 

  7. 7.

    J. Cracraft, M. Donoghue, Assembling the Tree of Life (Oxford University Press, USA, 2004)

    Google Scholar 

  8. 8.

    C. Dupuis, Annual Reviews in Ecology and Systematics 15, 1 (1984)

    MathSciNet  Google Scholar 

  9. 9.

    A. Rokas, Science 313, 1897 (2006)

    Article  Google Scholar 

  10. 10.

    E.A. Herrada, C.J. Tessone, V.M. Eguíluz, E. Hernández-García, C.M. Duarte, PLoS ONE 3, e2757 (2008)

    Article  Google Scholar 

  11. 11.

    E. Hernández-García, E.A. Herrada, A.F. Rozenfeld, C.J. Tessone, V.M. Eguíluz, C.M. Duarte, S. Arnaud-Haond, E. Serrão, Evolutionary and Ecological Trees and Networks, in XV Conference on Nonequilibrium Statistical Mechanics and Nonlinear Physics, edited by O. Descalzi, O.A. Rosso, H.A. Larrondo, AIP Conference Proceedings 913, 78 (2007)

  12. 12.

    L. Muchnik, R. Itzhack, S. Solomon, Y. Louzoun, Phys. Rev. E 76, 016106 (2007)

    Article  ADS  Google Scholar 

  13. 13.

    D.A. Huffman, Proceedings of the IRE 40, 1098 (1952)

    Article  Google Scholar 

  14. 14.

    D. Knuth, The art of computer programming, fundamental algorithms (AddisonWesley Longman Publishing Co., Inc. Redwood City, CA, USA, 1997), Vol. 1

    Google Scholar 

  15. 15.

    M. Goodrich, R. Tamassia, Algorithm Design: Foundations, Analysis, and Internet Examples (J. Wiley, 2002)

  16. 16.

    S. Golder, B. Huberman, J. Inf. Sci. 32, 198 (2006)

    Article  Google Scholar 

  17. 17.

    E. Codd, Communications of the ACM 13, 377 (1970)

    MATH  Article  Google Scholar 

  18. 18.

    K. Klemm, V.M. Eguíluz, M.S. Miguel, Phys. Rev. Lett. 95, 128701 (2005)

    Article  ADS  Google Scholar 

  19. 19.

    K. Klemm, V.M. Eguíluz, M.S. Miguel, Physica D: Nonlinear Phenomena 224, 149 (2006)

    MATH  Article  ADS  Google Scholar 

  20. 20.

    P.L. Krapivsky, S. Redner, F. Leyvraz, Phys. Rev. Lett. 85, 4629 (2000)

    Article  ADS  Google Scholar 

  21. 21.

    P.L. Krapivsky, S. Redner, Phys. Rev. E 63, 066123 (2001)

    Article  ADS  Google Scholar 

  22. 22.

    D. Garlaschelli, G. Caldarelli, L. Pietronero, Nature 423, 165 (2003)

    Article  ADS  Google Scholar 

  23. 23.

    D. Garlaschelli, G. Caldarelli, L. Pietronero, Nature E 4, 165 (2005)

    Article  Google Scholar 

  24. 24.

    S. Dorogovtsev, J. Mendes, A. Samukhin, Phys. Rev. Lett. 85, 4633 (2000)

    Article  ADS  Google Scholar 

  25. 25.

    P.L. Krapivsky, S. Redner, J. Phys. A 35, 9517 (2002)

    MATH  Article  MathSciNet  ADS  Google Scholar 

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Correspondence to M. M. Geipel.

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Geipel, M., Tessone, C. & Schweitzer, F. A complementary view on the growth of directory trees. Eur. Phys. J. B 71, 641 (2009). https://doi.org/10.1140/epjb/e2009-00302-5

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  • 64.60.aq Networks
  • 89.75.Fb Structures and organisation in complex systems
  • 89.75.Hc Networks and genealogical trees