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CS224W: Social and Information Network Analysis Jure Leskovec Stanford University Jure Leskovec, http://cs224w.stanford.edu

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[Morris 2000] Based on 2 player coordination game 2 players – each chooses technology A or B 10/11/2010 Jure Leskovec, Stanford CS224W: Social and Information Network Analysis, http://cs224w.stanford.edu 2
If both v and w adopt behavior A, they each get payoff a>0 If v and w adopt behavior B, they reach get payoff b>0 If v and w adopt the opposite behaviors opposite behaviors, they each get 0 10/11/2010 Jure Leskovec, Stanford CS224W: Social and Information Network Analysis, http://cs224w.stanford.edu 3

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Let v have d neighbors If fraction p of v ’s neighbors adopt A , then: v chooses A if: a p d > b (1 p) d 10/11/2010 Jure Leskovec, Stanford CS224W: Social and Information Network Analysis, http://cs224w.stanford.edu 4
Payoffs: a=3 b=2 Threshold: Payoffs: a 3, b 2 Everyone is adopting B v and w are initial adopters q b a b p Does the adoption spread? Fact: When a node switches from B to A it never wants to switch back to B . 10/11/2010 Jure Leskovec, Stanford CS224W: Social and Information Network Analysis, http://cs224w.stanford.edu 5

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Consider infinite graph G (but each node has finite number of neighbors) We say that a finite set S causes a cascade in G with threshold q if, when S adopts A, eventually every node adopts A Example: Path 10/11/2010 Jure Leskovec, Stanford CS224W: Social and Information Network Analysis, http://cs224w.stanford.edu 6
Tree: Grid: 10/11/2010 Jure Leskovec, Stanford CS224W: Social and Information Network Analysis, http://cs224w.stanford.edu 7

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Def: The cascade threshold of a graph G is the Def: The cascade threshold of a graph largest q
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