Geodesic
About the power law of the PageRank vector distribution. Part~2. Backley--Osthus model, power law verification for this model and setup of real search engines
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 21 (2018) no. 1, pp. 23-45

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In the second part of this paper, we consider the Buckley–Osthus model for the formation of a webgraph. For the networks generated according to this model, we numerically calculate the PageRank vector. We show that the components of this vector are distributed according to the power law. We also discuss the computational aspects of this model with respect to different numerical methods for the calculation of the PageRank vector, presented in the first part of the paper. Finally, we describe a general model for the web-page ranking and some approaches to solve the optimization problem arising when learning this model. 
@article{SJVM_2018_21_1_a1,
     author = {A. Gasnikov and P. Dvurechensky and M. Zhukovskii and S. Kim and S. Plaunov and D. Smirnov and F. Noskov},
     title = {About the power law of the {PageRank} vector distribution. {Part~2.} {Backley--Osthus} model, power law verification for this model and setup of real search engines},
     journal = {Sibirskij \v{z}urnal vy\v{c}islitelʹnoj matematiki},
     pages = {23--45},
     publisher = {mathdoc},
     volume = {21},
     number = {1},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJVM_2018_21_1_a1/}
}
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%A P. Dvurechensky
%A M. Zhukovskii
%A S. Kim
%A S. Plaunov
%A D. Smirnov
%A F. Noskov
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%J Sibirskij žurnal vyčislitelʹnoj matematiki
%D 2018
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%F SJVM_2018_21_1_a1
A. Gasnikov; P. Dvurechensky; M. Zhukovskii; S. Kim; S. Plaunov; D. Smirnov; F. Noskov. About the power law of the PageRank vector distribution. Part~2. Backley--Osthus model, power law verification for this model and setup of real search engines. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 21 (2018) no. 1, pp. 23-45. http://geodesic.mathdoc.fr/item/SJVM_2018_21_1_a1/