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Back to Markov chains and Google's PageRank algorithm

Exercise 5

Avg difficulty 2.5

Explain your responses to the following.

  1. Why does Google use a Markov chain to compute the PageRank vector?

  2. Describe two problems that can happen when Google constructs a Markov chain using the Google matrix GG.

  3. Describe how these problems are consistent with the Perron-Frobenius theorem.

  4. Describe why the Perron-Frobenius theorem suggests creating a Markov chain using the modified Google matrix G′=αG+(1−α)HnG' = \alpha G + (1-\alpha)H_n.

Austin, Understanding Linear Algebra, §4.5 Markov chains and Google's PageRank algorithm, Exercise 5

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Adapted from Understanding Linear Algebra © 2023 David Austin. Licensed under CC BY 4.0. Source: Understanding Linear Algebra. Imported at revision 3e6dced.