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MathematicsforComputerScience GoogleRankings MIT 6.042J/18.062J Which webpages are more important? PageRank Model of internet: Users click random link on a page. (byGooglefounder Occasionally start over. LarryPage) A

SLIDE 1

Mathematics for Computer Science

MIT 6.042J/18.062J

PageRank

(by Google founder Larry Page)

Google Rankings

Which webpages are “more important?” Model of internet:

Users click random link on a page.
Occasionally start over.

A page is “more important” if viewed a large fraction of time

pagerank.1 pagerank.2 Albert R Meyer, May 13, 2015 Albert R Meyer, May 13, 2015

Random Walk on the Web Random Walk on the Web

View the entire web as digraph

vertices are webpages
edge (V,W) exists if link from

page V to page W

edges out of V equally likely

Pr[(V,W)] = 1/outdeg(V)

To model starting over: * add a “supernode” to the graph * an edge from supernode to each

ther node

* edges from each other node back to supernode may get customized probabilities

pagerank.3 pagerank.4 Albert R Meyer, May 13, 2015 Albert R Meyer, May 13, 2015

SLIDE 2

T T T

pagerank.5 Albert R Meyer, May 13, 2015

Super-node

½ ½

T H T T

win

T H H T H

lose

T H H T super

pagerank.6

Compute stationary distribution PageRank(V) ::= sV Rank V above W when sV > sW

Albert R Meyer, May 13, 2015

s

PageRank

* Creating fake nodes pointing to self * Adding links to important nodes

won’t improve PageRank

pagerank.7 Albert R Meyer, May 13, 2015

Resistance to scamming

ensures * unique stable distribution * every initial distribution converges to * convergence is rapid: t is small so easy to compute

Importance of Super-node

pagerank.8 Albert R Meyer, May 13, 2015

s

p

s

lim

t→∞ p

⋅Mt = s

s

SLIDE 3

Actual Google Rank Google rank rules are a closely held trade secret using text, location, payment, and other criteria that have evolved for 15 years. But PageRank continues to play a significant role.

pagerank.9 Albert R Meyer, May 13, 2015

SLIDE 4

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6.042J / 18.062J Mathematics for Computer Science

Spring 2015 For information about citing these materials or our Terms of Use, visit: https://ocw.mit.edu/terms.