A complementary view on the growth of directory trees

  • M. M. GeipelEmail author
  • C. J. Tessone
  • F. Schweitzer
Topical issue on The Physics Approach to Risk: Agent-Based Models and Networks


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.

PACS Networks 89.75.Fb Structures and organisation in complex systems 89.75.Hc Networks and genealogical trees 


  1. 1.
    G. Caldarelli, Scale-Free Networks (Oxford University Press, 2007)Google Scholar
  2. 2.
    I. Rodríguez-Iturbe, A. Rinaldo, Fractal River Basins: Chance and Self-Organization (Cambridge University Press, 1997)Google Scholar
  3. 3.
    M. Zamir, J. Theor. Biol. 197, 517 (1999)CrossRefGoogle 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)CrossRefADSGoogle Scholar
  6. 6.
    P. Prusinkiewicz, A. Lindenmayer, The algorithmic beauty of plants (Springer-Verlag, Inc., New York, NY, USA, 1990)zbMATHGoogle 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)MathSciNetGoogle Scholar
  9. 9.
    A. Rokas, Science 313, 1897 (2006)CrossRefGoogle Scholar
  10. 10.
    E.A. Herrada, C.J. Tessone, V.M. Eguíluz, E. Hernández-García, C.M. Duarte, PLoS ONE 3, e2757 (2008)CrossRefGoogle 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)Google Scholar
  12. 12.
    L. Muchnik, R. Itzhack, S. Solomon, Y. Louzoun, Phys. Rev. E 76, 016106 (2007)CrossRefADSGoogle Scholar
  13. 13.
    D.A. Huffman, Proceedings of the IRE 40, 1098 (1952)CrossRefGoogle Scholar
  14. 14.
    D. Knuth, The art of computer programming, fundamental algorithms (AddisonWesley Longman Publishing Co., Inc. Redwood City, CA, USA, 1997), Vol. 1Google Scholar
  15. 15.
    M. Goodrich, R. Tamassia, Algorithm Design: Foundations, Analysis, and Internet Examples (J. Wiley, 2002)Google Scholar
  16. 16.
    S. Golder, B. Huberman, J. Inf. Sci. 32, 198 (2006)CrossRefGoogle Scholar
  17. 17.
    E. Codd, Communications of the ACM 13, 377 (1970)zbMATHCrossRefGoogle Scholar
  18. 18.
    K. Klemm, V.M. Eguíluz, M.S. Miguel, Phys. Rev. Lett. 95, 128701 (2005)CrossRefADSGoogle Scholar
  19. 19.
    K. Klemm, V.M. Eguíluz, M.S. Miguel, Physica D: Nonlinear Phenomena 224, 149 (2006)zbMATHCrossRefADSGoogle Scholar
  20. 20.
    P.L. Krapivsky, S. Redner, F. Leyvraz, Phys. Rev. Lett. 85, 4629 (2000)CrossRefADSGoogle Scholar
  21. 21.
    P.L. Krapivsky, S. Redner, Phys. Rev. E 63, 066123 (2001)CrossRefADSGoogle Scholar
  22. 22.
    D. Garlaschelli, G. Caldarelli, L. Pietronero, Nature 423, 165 (2003)CrossRefADSGoogle Scholar
  23. 23.
    D. Garlaschelli, G. Caldarelli, L. Pietronero, Nature E 4, 165 (2005)CrossRefGoogle Scholar
  24. 24.
    S. Dorogovtsev, J. Mendes, A. Samukhin, Phys. Rev. Lett. 85, 4633 (2000)CrossRefADSGoogle Scholar
  25. 25.
    P.L. Krapivsky, S. Redner, J. Phys. A 35, 9517 (2002)zbMATHCrossRefMathSciNetADSGoogle Scholar

Copyright information

© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  1. 1.Chair of Systems Design, ETH ZurichZurichSwitzerland

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