AVERAGE DISTANCE IN GROWING TREES

K. Malarz (), J. Czaplicki, B. Kawecka-Magiera and K. Kułakowski ()
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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

International Journal of Modern Physics C (IJMPC), 2003, vol. 14, issue 09, 1201-1206

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.

Keywords: Exponential trees; scale-free networks; evolving networks; small-world effect (search for similar items in EconPapers)
Date: 2003
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DOI: 10.1142/S0129183103005315

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