Presentation Transcript

1. Social Networks 101

   Prof. Jason Hartline and Prof. Nicole Immorlica

2. Blog Posts

   Week 2
3. Diseases and Genes Poster: LalithPolepeddi About: Properties of a network Link: http://tinyurl.com/69e388/
4. The Minority Game Poster: SoumyaBonthu About: Game theory Link: www.unifr.ch/econophysics/minority/
5. Lecture Nine: Power laws and rich-get-richer phenomena
6. Numbers Your grades so far in this class The weight of an apple The temperature in Chicago on July 4th
7. Numbers Your grades so far in this class. The weight of an apple. The temperature in Chicago on July 4th. The height of a Dutch man. The speed of a car on I94. Most instances are typical. Seeing a rare number is very surprising.
8. Typical numbers These numbers are well-characterized by the average and the standard deviation.
9. Your grades in week one
10. Q. What is the largest city in the US? A. New York, population 8,310,212
11. Q. What is the 2nd largest city in the US? A. Los Angeles, population 3,834,340
12. Q. What is the 3rd largest city in the US? A. Chicago, population 2,836,658
13. City populations New York 8,310,212 Los Angeles 3,834,340 Chicago 2,836,658 Houston 2,208,180 Phoenix 1,552,259 Philadelphia 1,449,634 San Antonio 1,328,984 San Diego 1,266,731 Dallas 1,266,372 San Jose 939,899
14. City populations New York 8,310,212 Los Angeles 3,834,340 Chicago 2,836,658 230. Cambridge, MA 101,335 240. Gainesville, FL 95,447 250. McKinney, TX 54,369 A few cities with high population Many cities with low population
15. City populations
16. City populations
17. Power Law: The number of cities with population at least k is proportional to k-c for a constant c.
18. Power Law: The number of cities with population > k is proportional to k-c. “fraction of items” “popularity = k”
19. Power Law: Fraction f(k) of items with popularity k is proportional to k-c. f(k) k-c log [f(k)] log [k-c] log [f(k)] -c log [k]
20. A power law is a straight line on a log-log plot.
21. City populations
22. Other examples
23. Why does data exhibit power laws?
24. Previously, … Imitation Cascade
25. Today Imitation Power law
26. Constructing the web Pages are created in order, named 1, 2, …, N When created, page j links to a page by With probability p, picking a page i uniformly at random from 1, …, j-1 With probability (1-p), pick page i uniformly at random and link to the page that i links too Imitation
27. The rich get richer 2 b) With prob. (1-p), pick page i uniformly at random and link to the page that i links too 3/4 1/4
28. The rich get richer 2 b) With prob. (1-p), pick page i uniformly at random and link to the page that i links too Equivalently, 2 b) With prob. (1-p), pick a page proportional to its in-degree and link to it
29. Simulation
30. Optional material Rich get richer Power law
31. Why is Harry Potter popular? If we could re-play history, would we still read Harry Potter, or would it be some other book?
32. Information cascades and the rich Information cascade = so some people get a little bit richer by chance and then rich-get-richer dynamics = the random rich people get a lot richer very fast
33. Music download site – 8 worlds “Let’s go driving,” Barzin “Silence is sexy,” EinstürzendeNeubauten “Go it alone,” Noonday Underground “Picadilly Lilly,” Tiger Lillies “Let’s go driving,” Barzin “Silence is sexy,” EinstürzendeNeubauten “Go it alone,” Noonday Underground “Picadilly Lilly,” Tiger Lillies 18 59 3 7 47 10 2 1
34. Next time TBA