lecture07 - 2/24/2009 Importance in graphs COMPUTER SCIENCE...

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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 non-negative real number Sum over all nodes is 1 Let’s informally call a set of non-negative reals that sum to 1 a probability distribution Importance measures for web pages PageRank (Page and Brin) HITS (Kleinberg) Some easy examples Not a trivial problem Page with the most links to it? 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 ill-defined problem Walks in directed graphs Consider a “walk” on a graph Start somewhere, take an outgoing edge Do this repeatedly for a while Many intuitive examples of this 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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2/24/2009 2 Pirate-lite example “Generative model” for Pirate-speak 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 F goes from t={0,1,2…} to nodes F(0) = R 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 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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lecture07 - 2/24/2009 Importance in graphs COMPUTER SCIENCE...

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