Traditional and lazy pageranks for a line of nodes connected with complete graphs

• 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.

Subject headings

NATURVETENSKAP  -- Matematik -- Sannolikhetsteori och statistik (hsv//swe)

NATURAL SCIENCES  -- Mathematics -- Probability Theory and Statistics (hsv//eng)

Keyword

Graph

Lazy PageRank

PageRank

Random walk

Random processes

Stochastic systems

Websites

Complete graphs

Diverse methods

Explicit formula

Line graph

Numerical values

Graph theory

Mathematics/Applied Mathematics

matematik/tillämpad matematik

Publication and Content Type

ref (subject category)

kap (subject category)