Slides - SNAP - Stanford University

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Origins of a small-world idea: Bacon number: Create a network of Hollywood actors Connect two actors if they coappeared in the movie Bacon number: number of steps to Kevin Bacon As of Dec 2007, the highest (finite) Bacon number reported is 8 Only approx. 12% of all actors cannot be linked to Bacon 10/4/2011 Jure Leskovec, <strong>Stanford</strong> CS224W: Social and Information Network Analysis, http://cs224w.stanford.edu 33
Erdös numbers are small! 10/4/2011 Jure Leskovec, <strong>Stanford</strong> CS224W: Social and Information Network Analysis, http://cs224w.stanford.edu 34
Page 1 and 2: CS224W: Social and Information Netw
Page 3 and 4: Assume each node has d spokes (half
Page 5 and 6: S nodes α·S edges S’ nodes α·
Page 7 and 8: k-regular graph (every node has deg
Page 9 and 10: Proof (continued): Let S j be a se
Page 11 and 12: Degree distribution: ⎛n −1⎞ P
Page 13 and 14: Remember, expected degree E[ X v ]
Page 15 and 16: We just learned: P(I) = n e -c Let
Page 17: G np, n=100k, p(n-1) = 0.5 … 3 Fr
Page 20 and 21: Fraction of country’s population
Page 22 and 23: 10/4/2011 Jure Leskovec, Stanford C
Page 24 and 25: We plot the same data as on the pre
Page 26 and 27: MSN Messenger network Number of ste
Page 28: If G np is wrong, why did we spend
Page 33 and 34: 64 chains completed: (i.e., 64 lett
Page 35 and 36: In 2003 Dodds, Muhamad and Watts pe
Page 37 and 38: (1) What is the structure of a soci
Page 39 and 40: 10/4/2011 Jure Leskovec, Stanford C
Page 41 and 42: Consequence of expansion: Short pa
Page 43 and 44: Could a network with high clusterin
Page 45 and 46: High clustering High diameter N h =
Page 47 and 48: Alternative formulation of the mode
Page 49 and 50: Could a network with high clusterin

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