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Average Distance In Growing Trees

Author

Listed:
  • K. MALARZ

    (Department of Applied Computer Science, Faculty of Physics and Nuclear Techniques, AGH University of Science and Technology, al. Mickiewicza 30, PL-30059 Kraków, Poland)

  • J. CZAPLICKI

    (Department of Applied Computer Science, Faculty of Physics and Nuclear Techniques, AGH University of Science and Technology, al. Mickiewicza 30, PL-30059 Kraków, Poland)

  • B. KAWECKA-MAGIERA

    (Department of Applied Computer Science, Faculty of Physics and Nuclear Techniques, AGH University of Science and Technology, al. Mickiewicza 30, PL-30059 Kraków, Poland)

  • K. KUŁAKOWSKI

    (Department of Applied Computer Science, Faculty of Physics and Nuclear Techniques, AGH University of Science and Technology, al. Mickiewicza 30, PL-30059 Kraków, Poland)

Abstract

Two kinds of evolving trees are considered here: the exponential trees, where subsequent nodes are linked to old nodes without any preference, and the Barabási–Albert scale-free networks, where the probability of linking to a node is proportional to the number of its pre-existing links. In both cases, new nodes are linked tom=1nodes. The average node–node distancedis calculated numerically in evolving trees as dependent on the number of nodesN. The results forNnot less than a thousand are averaged over a thousand of growing trees. The results on the mean node–node distancedfor largeNcan be approximated byd=2ln(N)+c1for the exponential trees, andd=ln(N)+c2for the scale-free trees, whereciare constant. We also derive iterative equations fordand its dispersion for the exponential trees. The simulation and the analytical approach give the same results.

Suggested Citation

  • K. Malarz & J. Czaplicki & B. Kawecka-Magiera & K. Kułakowski, 2003. "Average Distance In Growing Trees," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 14(09), pages 1201-1206.
    • Handle: RePEc:wsi:ijmpcx:v:14:y:2003:i:09:n:s0129183103005315
    DOI: 10.1142/S0129183103005315
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