The Google Matrix (Cont.)

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The following table shows four different Google matrices and their corresponding PageRank vectors π, where the ith entry is the PageRank score for webpage i, for the directed graph on the right.

The table indicates that the personalization vector has more influence on the PageRank scores for smaller damping factors. For instance, when

• α=0.85 ⇒ the scores and the ordering of the scores differ significantly.
  
  
  • The first model assigns the uniform vector to v, and node 1 is one of the nodes with the lowest PageRank score.
  
  
  • The second model uses v=(1 0 0 0), and node 1 receives the highest score. This v suggests that when web surfers grow tired of following the Web’s link structure, they always move to node 1.

α=0.95 ⇒ the difference in PageRank scores and ordering of scores for these models is less significant. Even though v=(1 0 0 0) in the fourth model, the higher damping factor decreases the influence of v.