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Understanding PageRank Through Example Calculations and Document Authority Assessment

This lecture explores the PageRank algorithm, demonstrating its principles through a detailed example. We analyze how the ranking of documents A, B, C, and D evolves over several rounds, considering their link structures and resulting PageRank values. The session emphasizes key concepts of document authority, explaining why some documents rank higher than others based on the quantity and quality of incoming links. Join us to deepen your understanding of search engine optimization and the mathematical foundation of PageRank.

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Understanding PageRank Through Example Calculations and Document Authority Assessment

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  1. Lecture 17 Search Engines & Map Reduce Project meeting sign up: http://goo.gl/SauqD

  2. Page Rank Example A B C D A B C D A 0 1 0 0 B 1 0 0 1 C 1 1 0 1 D 1 0 1 0

  3. Page Rank Example A B C D A 0 1 0 0 B 1 0 0 1 C 1 1 0 1 D 1 0 1 0 Round 0 PR(A) = 1, PR(B) = 1, PR(C) = 1, PR(D) = 1 Round 1 PR(A) = 3 links to A

  4. Page Rank Example A B C D A 0 1 0 0 B 1 0 0 1 C 1 1 0 1 D 1 0 1 0 Round 0 PR(A) = 1, PR(B) = 1, PR(C) = 1, PR(D) = 1 Round 1 PR(A) = 1/2 + 3 links to A B links to 2 docs

  5. Page Rank Example A B C D A 0 1 0 0 B 1 0 0 1 C 1 1 0 1 D 1 0 1 0 Round 0 PR(A) = 1, PR(B) = 1, PR(C) = 1, PR(D) = 1 Round 1 PR(A) = 1/2 + 1/3 + 3 links to A B links to 2 docs C links to 3 docs

  6. Page Rank Example A B C D A 0 1 0 0 B 1 0 0 1 C 1 1 0 1 D 1 0 1 0 Round 0 PR(A) = 1, PR(B) = 1, PR(C) = 1, PR(D) = 1 Round 1 PR(A) = 1/2 + 1/3 + 1/2 = 1.33 3 links to A B links to 2 docs C links to 3 docs D links to 2 docs

  7. Page Rank Example A B C D A 0 1 0 0 B 1 0 0 1 C 1 1 0 1 D 1 0 1 0 Round 0 PR(A) = 1, PR(B) = 1, PR(C) = 1, PR(D) = 1 Round 1 PR(A) = 1/2 + 1/3 + 1/2 = 1.33 PR(B) = 2 links to B

  8. Page Rank Example A B C D A 0 1 0 0 B 1 0 0 1 C 1 1 0 1 D 1 0 1 0 Round 0 PR(A) = 1, PR(B) = 1, PR(C) = 1, PR(D) = 1 Round 1 PR(A) = 1/2 + 1/3 + 1/2 = 1.33 PR(B) = 1 + 1/3 = 1.33 2 links to B

  9. Page Rank Example A B C D A 0 1 0 0 B 1 0 0 1 C 1 1 0 1 D 1 0 1 0 Round 0 PR(A) = 1, PR(B) = 1, PR(C) = 1, PR(D) = 1 Round 1 PR(A) = 1/2 + 1/3 + 1/2 = 1.33 PR(B) = 1 + 1/3 = 1.33 PR(C) = .5 1 link to C

  10. Page Rank Example A B C D A 0 1 0 0 B 1 0 0 1 C 1 1 0 1 D 1 0 1 0 Round 0 PR(A) = 1, PR(B) = 1, PR(C) = 1, PR(D) = 1 Round 1 PR(A) = 1/2 + 1/3 + 1/2 = 1.33 PR(B) = 1 + 1/3 = 1.33 PR(C) = .5 PR(D) = 1/2 + 1/3 = .83 2 links to D

  11. Page Rank Example A B C D A 0 1 0 0 B 1 0 0 1 C 1 1 0 1 D 1 0 1 0 Round 1 PR(A) = 1.33, PR(B) = 1.33, PR(C) = .5, PR(D) = .83 Round 2 PR(A) = 1.33/2 + .5/3 + .83/2 = 1.24

  12. Page Rank Example A B C D A 0 1 0 0 B 1 0 0 1 C 1 1 0 1 D 1 0 1 0 Round 1 PR(A) = 1.33, PR(B) = 1.33, PR(C) = .5, PR(D) = .83 Round 2 PR(A) = 1.33/2 + .5/3 + .83/2 = 1.24 PR(B) = 1.33 + .5/3 = 1.49

  13. Page Rank Example A B C D A 0 1 0 0 B 1 0 0 1 C 1 1 0 1 D 1 0 1 0 Round 1 PR(A) = 1.33, PR(B) = 1.33, PR(C) = .5, PR(D) = .83 Round 2 PR(A) = 1.33/2 + .5/3 + .83/2 = 1.24 PR(B) = 1.33 + .5/3 = 1.49 PR(C) = .83 / 2 = .415

  14. Page Rank Example A B C D A 0 1 0 0 B 1 0 0 1 C 1 1 0 1 D 1 0 1 0 Round 1 PR(A) = 1.33, PR(B) = 1.33, PR(C) = .5, PR(D) = .83 Round 2 PR(A) = 1.33/2 + .5/3 + .83/2 = 1.24 PR(B) = 1.33 + .5/3 = 1.49 PR(C) = .83 / 2 = .415 PR(D) = 1.33/2 + .5/3 = .83

  15. Page Rank Example A B C D A 0 1 0 0 B 1 0 0 1 C 1 1 0 1 D 1 0 1 0 Round 1 PR(A) = 1.33, PR(B) = 1.33, PR(C) = .5, PR(D) = .83 Round 2 PR(A) = 1.24, PR(B) = 1.49, PR(C) = .415, PR(D) = .83 Round 3 PR(A) = 1.49/2 + .415/3 + .83/2 = 1.30 PR(B) = 1.24 + .415/3 = 1.37 PR(C) = .83/2 = .415 PR(D) = 1.49/2 + .415/3 = .883

  16. Page Rank Example A B C D A 0 1 0 0 B 1 0 0 1 C 1 1 0 1 D 1 0 1 0 Round 1 PR(A) = 1.33, PR(B) = 1.33, PR(C) = .5, PR(D) = .83 Round 2 PR(A) = 1.24, PR(B) = 1.49, PR(C) = .415, PR(D) = .83 Round 3 PR(A) = 1.30, PR(B) =1.37, PR(C) =.415, PR(D) =.883 Round(4) PR(A) = 1.37/2 + .415/3 + .883/2 = 1.27 PR(B) = 1.30 + .415/3 = 1.43 PR(C) = .883/2 = .441 PR(D) = 1.37/2 + .415/3 = .823

  17. Page Rank Example A B C D A 0 1 0 0 B 1 0 0 1 C 1 1 0 1 D 1 0 1 0 Round 1 PR(A) = 1.33, PR(B) = 1.33, PR(C) = .5, PR(D) = .83 Round 2 PR(A) = 1.24, PR(B) = 1.49, PR(C) = .415, PR(D) = .83 Round 3 PR(A) = 1.30, PR(B) =1.37, PR(C) =.415, PR(D) =.883 Round(4) PR(A) = 1.27, PR(B) = 1.43, PR(C) = .441, PR(D) = .823 Document(A) is good because lots of documents link to it Document(B) is good because A only links to it, and lots of people link to A (it's an authority) Document(C) is bad, because few people link to it , and it links to everyone Document(D) is ok

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