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Average distance in growing trees | | K.Malarz
; J.Czaplicki
; B.Kawecka-Magiera
; K.Kulakowski
; | | Date: |
28 Apr 2003 | | Journal: | Int. J. Mod. Phys. C14 (2003) 1201 DOI: 10.1142/S0129183103005315 | | Subject: | Statistical Mechanics; Disordered Systems and Neural Networks | cond-mat.stat-mech cond-mat.dis-nn | | 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 to $m=1$ nodes. Average node-node distance $d$ is calculated numerically in evolving trees as dependent on the number of nodes $N$. The results for $N$ not less than a thousand are averaged over a thousand of growing trees. The results on the mean node-node distance $d$ for large $N$ can be approximated by $d=2ln(N)+c_1$ for the exponential trees, and $d=ln(N)+c_2$ for the scale-free trees, where the $c_i$ are constant. We derive also iterative equations for $d$ and its dispersion for the exponential trees. The simulation and the analytical approach give the same results. | | Source: | arXiv, cond-mat/0304636 | | Services: | Forum | Review | PDF | Favorites | |
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