1. Google PageRank Algorithm
By: Danny Lin

2. Table of Contents Google Search History / What is Page Rank?
Page Rank Algorithm
Inbound/Outbound Links
Dangling Nodes
Constraints
Calculating your page rank
How to maximize your page rank score
Loopholes
Neat stuff

3. Google Search Google search using PageRank:
1) Crawl the web and locate all publicly accessible webpages
2) Index the data from step 1 to allow for efficient searches for keywords or phrases
3) Rate the importance of each page in the database – using PageRank
4) Return results in descending order of importance with respect to search

4. Google’s Original Architectural Design
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5. History
Page Rank was conceptualized by Sergey Brin and Lawrence Page; discussed in their paper: The anatomy of a large-scale hypertextual web search engine (
Used to rank the importance of web pages
Source:

6. PR(A) = (1-d) + d(PR(T1)/C(T1) + … + PR(Tn)/C(Tn))
Page Rank Algorithm
PR(A) = (1-d) + d(PR(T1)/C(T1) + … + PR(Tn)/C(Tn))
PR(Tn) - The importance of page Tn.
C(Tn) - The number of outgoing links for page Tn.
PR(Tn)/C(Tn) - The calculated importance passed to page A from page Tn.
d - damping factor (0.85).

7. Inbound/Outbound Links
With respect to page A:
Inbound links – links that point towards page A
Outbound links – links within page A pointing towards other pages

8. Dangling Nodes
A dangling node is a page that does not have any outbound links.
Issue: They act as sinks that reduce the importance from the web.
Solution: Assume that the dangling node has a link to every other page. We randomly select the next page at random. This creates a stochastic matrix; all entries are nonnegative and the sum of each column is equal to 1.
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9. Constraints
Must be primitive, i.e. for some n, Sn has all positive entries where λ1 = 1 and λ2 < 1
Must be stochastic, i.e. all entries are nonnegative and the sum of each column is equal to 1.
Must be irreducible, i.e. you should not be able to perform row/column permutations such that you end up with a block upper-triangular form. The nodes must be strongly connected.

10. Calculating your page rank
“Page Rank can be calculated using a simple iterative algorithm and corresponds to the principal eigenvector of the normalized link matrix (probability distribution) of the web”
Algorithm to calculate the normalized probability distribution:
Multiply stochastic matrix, S, with an random eigenvector, i1, to get new eigenvector, i2…
Repeat step 1 until in-1 = in (approx.)
LINEAR ALGEBRA TIME!!! Page Rank calculation time!

11. How to maximize your page rank score
Internal Linking – having links to other pages within your website
Hierarchical
Fully meshed
Good and plentiful content
E.g. news website
Provide a useful service or product
E.g. phpbb – online bulletin board system

12. Loopholes
SEO (Search Engine Optimization) webpages to increase traffic flow  conversions  $$
An issues that arose from this: the selling of links from high PR pages
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13. Neat stuff Overview of a google search (1-2 minutes):
How search has evolved (6 minutes):
Changes to Google’s search algorithm:

14. References
Content
Images

15. Questions?
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