PageRank, Connecting a Line of Nodes with a Complete Graph

  • Christopher EngströmEmail author
  • Sergei Silvestrov
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 179)


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.


PageRank Graph Random walk Block matrix 



This research was supported in part by the Swedish Research Council (621- 2007-6338), Swedish Foundation for International Cooperation in Research and Higher Education (STINT), Royal Swedish Academy of Sciences, Royal Physiographic Society in Lund and Crafoord Foundation.


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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Division of Applied Mathematics, School of Education, Culture and CommunicationMälardalen UniversityVästeråsSweden

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