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PageRank, connecting a line of nodes with multiple complete graphs
Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. (MAM)ORCID iD: 0000-0001-7822-2103
Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. (MAM)
Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. (MAM)ORCID iD: 0000-0002-1624-5147
Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. (MAM)ORCID iD: 0000-0003-4554-6528
2017 (English)In: Proceedings of the 17th Applied Stochastic Models and Data Analysis International Conference with the 6th Demographics Workshop, London, UK: June 6-9, 2017. / [ed] Christos H Skiadas, ISAST: International Society for the Advancement of Science and Technology , 2017, p. 113-126Conference paper, Published paper (Refereed)
Abstract [en]

PageRank was initially defined by S. Brin and L. Page for the purpose of ranking homepages (nodes) based on the structure of links between these pages. Studies has shown that PageRank of a graph changes with changes in the structure of the graph. In this article, we examine how the PageRank changes when two or more outside nodes are connected to a line directed graph. We also look at the PageRank of a graph resulting from connecting a line graph to two complete graphs. In this paper we demonstrate that both the probability (or random walk on a graph) and blockwise matrix inversion approaches can be used to determine explicit formulas for the PageRanks of simple networks.

Place, publisher, year, edition, pages
ISAST: International Society for the Advancement of Science and Technology , 2017. p. 113-126
National Category
Engineering and Technology
Research subject
Mathematics/Applied Mathematics
Identifiers
URN: urn:nbn:se:mdh:diva-51328ISBN: 978-618-5180-23-2 (electronic)OAI: oai:DiVA.org:mdh-51328DiVA, id: diva2:1474393
Conference
The 17th Applied Stochastic Models and Data Analysis International Conference with the 6th Demographics Workshop (ASMDA2017).
Note

Authors: Pitos Seleka Biganda, Benard Abola, Christopher Engström, Sergei Silvestrov.

Available from: 2020-10-08 Created: 2020-10-08 Last updated: 2020-11-10Bibliographically approved
In thesis
1. Analytical and Iterative Methods of Computing PageRank of Networks
Open this publication in new window or tab >>Analytical and Iterative Methods of Computing PageRank of Networks
2020 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

This thesis is about variants of PageRank, methods of PageRank computation and perturbation analysis of a PageRank vector as a stationary distribution of a kind of perturbed Markov chain model. 

Chapter 2 of this thesis gives closed form formulae for ordinary and lazy PageRanks for some specific simple line graphs. Different cases of changes made to the simple line graph are considered and for each case, a corresponding formula for each of the two variants of PageRank is provided.

Chapter 3 is dedicated to the exploration of relationships that exist between three known variants of PageRank: ordinary PageRank, lazy PageRank and random walk with backstep PageRank in terms of their convergence and consistency in rank scores for different graph structures with reference to PageRank parameters, the damping factor c and backstep parameter β. 

In Chapter 4, we discuss numerical methods used in solving the PageRank problem as a linear system and evaluate some stopping criteria that can be employed in such methods. 

Finally, in Chapter 5, we address the PageRank problem as a first order perturbed Markov chain problem and study the perturbation analysis for stationary distributions of Markov chains with damping component. We illustrate our results on asymptotic perturbation analysis by using different computational examples.

Place, publisher, year, edition, pages
Västerås: Mälardalen University, 2020
Series
Mälardalen University Press Dissertations, ISSN 1651-4238 ; 325
National Category
Probability Theory and Statistics
Research subject
Mathematics/Applied Mathematics
Identifiers
urn:nbn:se:mdh:diva-51390 (URN)978-91-7485-482-4 (ISBN)
Public defence
2020-11-20, Kappa +(Zoom), Mälardalens högskola, Västerås, 10:15 (English)
Opponent
Supervisors
Available from: 2020-10-09 Created: 2020-10-08 Last updated: 2020-11-09Bibliographically approved

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http://www.asmda.es/asmda2017.html

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Biganda, Pitos SelekaAbola, BenardEngström, ChristopherSilvestrov, Sergei

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