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2/24/2009
1
COMPUTER SCIENCE 51
Spring 2009
cs51.seas.harvard.edu
Prof. Greg Morrisett
Prof. Ramin Zabih
Importance in graphs
•
What makes a node “important”?
–
More precisely: assign to each node a
nonnegative real number
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Sum over all nodes is 1
•
Let’s informally call a set of nonnegative reals
that sum to 1 a
probability distribution
•
Importance measures for web pages
–
PageRank (Page and Brin)
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HITS (Kleinberg)
Some easy examples
Not a trivial problem
•
Page with the most links to it?
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Advantage: Easy to compute!
–
Disadvantage: Doesn’t work very well
•
Not all links are created equal
–
Having a link from the NYT or Harvard
home page is much more important than
a link from the CS51 home page
•
“A page is important if it has hyperlinks from
important pages” (recursion!)
•
Right math for an illdefined problem
Walks in directed graphs
•
Consider a “walk” on a graph
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Start somewhere, take an outgoing edge
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Do this repeatedly for a while
•
Many intuitive examples of this
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Quite important in advanced CS classes
–
Also: statistics, math, EE, etc.
Map example
•
Note: only some edges shown in this example
Your room
Corridor
Fire
escape
Entryway
Street
Harvard
Yard
Maxwel
Dworkin
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Piratelite example
•
“Generative model” for Piratespeak
–
Reflects a
grammar
and
parser
also!
“Avast!”
“Ye”
“Yon”
“salty”
“scurvy”
“wel
dressed”
“TFs”
“students”
“faculty?!”
“CS51”
What is a walk on a graph?
•
A walk from an initial node R on a
graph is a function F such that
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F goes from t={0,1,2…} to nodes
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F(0) = R
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If F(i) = v and F(i+1) = v’, then there is an
edge from v to v’
•
Note: HOP examples abound
–
Given a graph, return a walk
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Given a graph and a function, check
that function is a walk (to depth n)
What do walks represent?
•
So far: permitted states of affairs
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 Spring '09
 GREGMORRISETT

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