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PageRank, Connecting a Line of Nodes with a Complete GraphPrimeFaces.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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PrimeFaces.cw("AccordionPanel","widget_formSmash_responsibleOrgs",{id:"formSmash:responsibleOrgs",widgetVar:"widget_formSmash_responsibleOrgs",multiple:true}); 2016 (English)In: Engineering Mathematics II: Algebraic, Stochastic and Analysis Structures for Networks, Data Classification and Optimization / [ed] Sergei Silvestrov; Milica Rancic, Springer, 2016Chapter in book (Refereed)
##### Abstract [en]

##### Place, publisher, year, edition, pages

Springer, 2016.
##### Series

Springer Proceedings in Mathematics and Statistics, ISSN 2194-1009 ; 179
##### Keyword [en]

PageRank, random walk, graph, linear system, subgraph
##### National Category

Computational Mathematics Discrete Mathematics Probability Theory and Statistics
##### Research subject

Mathematics/Applied Mathematics
##### Identifiers

URN: urn:nbn:se:mdh:diva-33379DOI: 10.1007/978-3-319-42105-6ISBN: 978-3-319-42104-9 (print)ISBN: 978-3-319-42105-6 (print)OAI: oai:DiVA.org:mdh-33379DiVA: diva2:1034023
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Available from: 2016-10-11 Created: 2016-10-11 Last updated: 2016-12-05Bibliographically approved
##### In thesis

The focus of this article is the PageRank algorithm originally defined by S. Brin and L. Page as the stationary distribution of a certain random walk on a graph used to rank homepages on the Internet. We will attempt to get a better understanding of how PageRank changes after you make some changes to the graph such as adding or removing edge between otherwise disjoint subgraphs. In particular we will take a look at link structures consisting of a line of nodes or a complete graph where every node links to all others and different ways to combine the two. Both the ordinary normalized version of PageRank as well as a non-normalized version of PageRank found by solving corresponding linear system will be considered. We will see that it is possible to find explicit formulas for the PageRank in some simple link structures and using these formulas take a more in-depth look at the behavior of the ranking as the system changes.

1. PageRank in Evolving Networks and Applications of Graphs in Natural Language Processing and Biology$(function(){PrimeFaces.cw("OverlayPanel","overlay1039463",{id:"formSmash:j_idt707:0:j_idt711",widgetVar:"overlay1039463",target:"formSmash:j_idt707:0:parentLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

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