Abstract
We consider a scale-free model of the Web network that is evolving by preferential attachment schemes and derive an explicit formula of its PageRank vector. Its \(i^{th}\) element indicates the probability that a surfer resides at a related Web page i in a stationary regime of an associated random walk. Considering the growth of a directed Web graph, we apply linear preferential attachment schemes proposed by Samorodnitsky et al. (2016). To express the probability of a connection between two nodes of this Web graph, our derivation allows us to avoid the consideration of complicated paths with random lengths and to cover both self-loops and multiple edges between nodes. An algorithm of the PageRank vector calculation for graphs without loops is provided. The approach can be extended in a similar way to graphs with loops. In this way, our approach enhances existing analysis schemes. It provides a better insight on the PageRank of growing scale-free Web networks and supports the adaptation of the model to gathered network statistics.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Brin, S., Page, L.: The anatomy of a large-scale hypertextual web search engine. Comput. Netw. ISDN Syst. 30(1–7), 107–117 (1998)
Fortunato, S., Boguñá, M., Flammini, A., Menczer, F.: Approximating PageRank from in-degree. In: Aiello, W., Broder, A., Janssen, J., Milios, E. (eds.) WAW 2006. LNCS, vol. 4936, pp. 59–71. Springer, Heidelberg (2008). https://doi.org/10.1007/978-3-540-78808-9_6
Litvak, N., Scheinhardt, W.R.W., Volkovich, Y.: In-degree and PageRank: why do they follow similar power laws? Internet Math. 4(2–3), 175–198 (2007)
Chen, N., Litvak, N., Olvera-Cravioto, M.: PageRank in scale-free random graphs. In: Bonato, A., Graham, F.C., Prałat, P. (eds.) WAW 2014. LNCS, vol. 8882, pp. 120–131. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-13123-8_10
Fortunato, S., Boguñá, M., Flammini, A., Menczer, F.: On local estimations of PageRank: a mean field approach. Internet Math. 4(2–3), 245–266 (2007)
Avrachenkov, K., Lebedev, D.: PageRank of scale-free growing networks. Internet Math. 3(2), 207–231 (2006)
Samorodnitsky, G., Resnick, S., Towsley, D., Davis, R., Willis, A., Wan, P.: Nonstandard regular variation of in-degree and out-degree in the preferential attachment model. J. Appl. Prob. 53(1), 146–161 (2016)
Wan, P., Wang, T., Davis, R.A., et al.: Are extreme value estimation methods useful for network data? Extremes 23, 171–195 (2020). https://doi.org/10.1007/s10687-019-00359-x
Langville, A.N., Meyer, C.D.: Deeper inside PageRank. Internet Math. 1(3), 335–380 (2005)
Acknowledgments
The first author was partly supported by Russian Foundation for Basic Research (grant 19-01-00090).
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2021 Springer Nature Switzerland AG
About this paper
Cite this paper
Markovich, N.M., Krieger, U.R. (2021). The PageRank Vector of a Scale-Free Web Network Growing by Preferential Attachment. In: Vishnevskiy, V.M., Samouylov, K.E., Kozyrev, D.V. (eds) Distributed Computer and Communication Networks: Control, Computation, Communications. DCCN 2021. Lecture Notes in Computer Science(), vol 13144. Springer, Cham. https://doi.org/10.1007/978-3-030-92507-9_3
Download citation
DOI: https://doi.org/10.1007/978-3-030-92507-9_3
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-92506-2
Online ISBN: 978-3-030-92507-9
eBook Packages: Computer ScienceComputer Science (R0)