Number of maximal rooted trees in preferential attachment model via stochastic approximation
Vestnik Tverskogo gosudarstvennogo universiteta. Seriâ Prikladnaâ matematika, no. 2 (2023), pp. 28-36
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We study the asymptotic behavior of the number of maximal trees in the preferential attachment model. In our model, we consider a sequence of graphs built by the following recursive rule. We start with the complete graph on $m+1$ vertices, $m>1$. Then on the $n+1$ step, we add vertex $n+1$ and draw $m$ edges from it to different vertices from $1,\ldots,n$, chosen with probabilities proportional to their degrees plus some positive parameter $\beta$. We prove the convergence speed for the number of maximal trees in such a model using the stochastic approximation technique.
Keywords:
random graphs, preferential attachment, stochastic approximation.
@article{VTPMK_2023_2_a2,
author = {Yu. A. Malyshkin},
title = {Number of maximal rooted trees in preferential attachment model via stochastic approximation},
journal = {Vestnik Tverskogo gosudarstvennogo universiteta. Seri\^a Prikladna\^a matematika},
pages = {28--36},
publisher = {mathdoc},
number = {2},
year = {2023},
language = {en},
url = {http://geodesic.mathdoc.fr/item/VTPMK_2023_2_a2/}
}
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Yu. A. Malyshkin. Number of maximal rooted trees in preferential attachment model via stochastic approximation. Vestnik Tverskogo gosudarstvennogo universiteta. Seriâ Prikladnaâ matematika, no. 2 (2023), pp. 28-36. http://geodesic.mathdoc.fr/item/VTPMK_2023_2_a2/