Traditional and Lazy PageRanks for a Line of Nodes Connected with Complete Graphs

  • Pitos Seleka BigandaEmail author
  • Benard Abola
  • Christopher Engström
  • John Magero Mango
  • Godwin Kakuba
  • Sergei Silvestrov
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 271)


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.


Graph Random walk PageRank Lazy PageRank 



This research was supported by the Swedish International Development Cooperation Agency (Sida), International Science Programme (ISP) in Mathematical Sciences (IPMS), Sida Bilateral Research Program (Makerere University and University of Dar-es-Salaam). We are also grateful to the research environment Mathematics and Applied Mathematics (MAM), Division of Applied Mathematics, Mälardålen University for providing an excellent and inspiring environment for research education and research. The authors are grateful to Dmitrii Silvestrov for useful comments and discussions.


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Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  • Pitos Seleka Biganda
    • 1
    • 2
    Email author
  • Benard Abola
    • 1
    • 3
  • Christopher Engström
    • 1
  • John Magero Mango
    • 3
  • Godwin Kakuba
    • 3
  • Sergei Silvestrov
    • 1
  1. 1.Division of Applied Mathematics, School of Education, Culture and CommunicationMälardalen UniversityVästeråsSweden
  2. 2.Department of Mathematics, College of Natural and Applied SciencesUniversity of Dar es SalaamDar es SalaamTanzania
  3. 3.Department of Mathematics, School of Physical SciencesMakerere UniversityKampalaUganda

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