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Traditional and lazy pageranks for a line of nodes connected with complete graphs
Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. Department of Mathematics, College of Natural and Applied Sciences, University of Dar es Salaam,Tanzania. (MAM)
Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. Department of Mathematics, School of Physical Sciences, Makerere University, Kampala, Uganda. (MAM)
Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. (MAM)ORCID iD: 0000-0002-1624-5147
Department of Mathematics, School of Physical Sciences, Makerere University, Kampala, Uganda.
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2018 (English)In: Stochastic Processes and Applications: SPAS2017, Västerås and Stockholm, Sweden, October 4-6, 2017 / [ed] Sergei Silvestrov, Anatoliy Malyarenko, Milica Rančić, Springer, 2018, Vol. 271, p. 391-412Chapter in book (Refereed)
Abstract [en]

PageRank was initially defined by S. Brin and L. Page for the purpose of measuring the importance of web pages (nodes) based on the structure of links between them. Due to existence of diverse methods of random walk on the graph, variants of PageRank now exists. They include traditional (or normal) PageRank due to normal random walk and Lazy PageRank due to lazy random walk on a graph. In this article, we establish how the two variants of PageRank changes when complete graphs are connected to a line of nodes whose links between the nodes are in one direction. Explicit formulae for the two variants of PageRank are presented. We have noted that the ranks on a line graph are the same except their numerical values which differ. Further, we have observed that both normal random walk and lazy random walk on complete graphs spend almost the same time at each node.

Place, publisher, year, edition, pages
Springer, 2018. Vol. 271, p. 391-412
Series
Springer Proceedings in Mathematics and Statistics, ISSN 2194-1009
Keywords [en]
Graph, Lazy PageRank, PageRank, Random walk, Random processes, Stochastic systems, Websites, Complete graphs, Diverse methods, Explicit formula, Line graph, Numerical values, Graph theory
National Category
Mathematics
Research subject
Mathematics/Applied Mathematics
Identifiers
URN: urn:nbn:se:mdh:diva-41835DOI: 10.1007/978-3-030-02825-1_17Scopus ID: 2-s2.0-85058552957ISBN: 978-3-030-02824-4 (print)OAI: oai:DiVA.org:mdh-41835DiVA, id: diva2:1274023
Conference
International Conference on “Stochastic Processes and Algebraic Structures – From Theory Towards Applications”, SPAS 2017; Västerås and Stockholm; Sweden; 4 October 2017 through 6 October 2017; Code 221789
Available from: 2018-12-27 Created: 2018-12-27 Last updated: 2018-12-31Bibliographically approved

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Publisher's full textScopushttps://www.springer.com/gp/book/9783030028244

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Biganda, PitosAbola, BenardEngström, ChristopherSilvestrov, Sergei

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