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#### Open Access in DiVA

####

#### Authority records

Seleka Biganda, Pitos
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Seleka Biganda, Pitos
##### By organisation

Educational Sciences and Mathematics
On the subject

Probability Theory and Statistics
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Analytical and Iterative Methods of Computing PageRank of NetworksPrimeFaces.cw("AccordionPanel","widget_formSmash_some",{id:"formSmash:some",widgetVar:"widget_formSmash_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_all",{id:"formSmash:all",widgetVar:"widget_formSmash_all",multiple:true});
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2020 (English)Doctoral thesis, comprehensive summary (Other academic)
##### Abstract [en]

##### 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: urn:nbn:se:mdh:diva-51390ISBN: 978-91-7485-482-4 (print)OAI: oai:DiVA.org:mdh-51390DiVA, id: diva2:1474498
##### Public defence

2020-11-20, Kappa +(Zoom), Mälardalens högskola, Västerås, 10:15 (English)
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#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt506",{id:"formSmash:j_idt506",widgetVar:"widget_formSmash_j_idt506",multiple:true}); Available from: 2020-10-09 Created: 2020-10-08 Last updated: 2020-11-09Bibliographically approved
##### List of papers

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.

1. Perturbation analysis for stationary distributions of markov chains with damping component$(function(){PrimeFaces.cw("OverlayPanel","overlay1454271",{id:"formSmash:j_idt563:0:j_idt567",widgetVar:"overlay1454271",target:"formSmash:j_idt563:0:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

2. Perturbed Markov Chains with Damping Component$(function(){PrimeFaces.cw("OverlayPanel","overlay1469236",{id:"formSmash:j_idt563:1:j_idt567",widgetVar:"overlay1469236",target:"formSmash:j_idt563:1:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

3. PageRank, connecting a line of nodes with multiple complete graphs$(function(){PrimeFaces.cw("OverlayPanel","overlay1474393",{id:"formSmash:j_idt563:2:j_idt567",widgetVar:"overlay1474393",target:"formSmash:j_idt563:2:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

4. Traditional and lazy pageranks for a line of nodes connected with complete graphs$(function(){PrimeFaces.cw("OverlayPanel","overlay1274023",{id:"formSmash:j_idt563:3:j_idt567",widgetVar:"overlay1274023",target:"formSmash:j_idt563:3:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

5. Exploring The Relationship Between Ordinary PageRank, Lazy PageRank and Random Walk with Backstep PageRank for Different Graph Structures$(function(){PrimeFaces.cw("OverlayPanel","overlay1472510",{id:"formSmash:j_idt563:4:j_idt567",widgetVar:"overlay1472510",target:"formSmash:j_idt563:4:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

6. Nonlinearly Perturbed Markov Chains and Information Networks$(function(){PrimeFaces.cw("OverlayPanel","overlay1394752",{id:"formSmash:j_idt563:5:j_idt567",widgetVar:"overlay1394752",target:"formSmash:j_idt563:5:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

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8. Evaluation of Stopping Criteria for Ranks in Solving Linear Systems$(function(){PrimeFaces.cw("OverlayPanel","overlay1385948",{id:"formSmash:j_idt563:7:j_idt567",widgetVar:"overlay1385948",target:"formSmash:j_idt563:7:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

isbn
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