Social Networks 101

1. Social Networks 101 Prof. Jason Hartline and Prof. Nicole Immorlica

2. Recap Social Goal. Explain why information and disease spread so quickly in social networks. Mathematical Approach. Model social networks as random graphs and argue that they are likely to have low diameter.

3. Random graph diameter Technique. Grow trees to bound path lengths. • Show when trees are small enough (< √n), # of leaves doubles. • Grow small trees (< √n) around a pair of nodes. • Use birthday paradox to argue trees prob. intersect. Conclude diameter is 2 log √n = log n.

4. Lecture Five: How do people find each other in a social network?

5. Movie time.

6. Small world phenomenon Milgram’sexperiment (1960s). Ask someone to pass a letter to another person via friends knowing only the name, address, and occupation of the target.

7. Small world phenomenon Bernard, David’s cousin who went to college with David, mayor of Bob’s town Bob, a farmer in Nebraska Maya, who grew up in Boston With Lashawn

8. Last time: short paths exist. (argument: flood the network)

9. This time: and people can find short paths! (without flooding the network)

10. The Milgram experiment Experiment: We choose a random “source” and “target”. Your goal: pass ball from “source” to “target” by throwing it to people you know on a first-name basis.

11. How did you find short paths?

12. What information did you use to choose the next hop?

13. Social network models Random rolodex model Random wiring model

14. Random wiring model People have a predictable structure of local links (e.g., neighbors, colleagues) And a few random long-range links (e.g., someone you meet on a trip)

15. Random wiring model Local links have grid-like structure (you know the person on your left/right and front/back) n n

16. Random wiring model Local links represent homophily, the idea that we know people similar to us n n

17. Random wiring model Long-range links are random – each node chooses one long-range link n n

18. Random wiring model Long-range links represent weak ties, the links to acquantainces that would otherwise be far away n n

19. Random wiring model What do you expect the diameter to be? Do you expect people to find short paths? If so, how short?

20. Short paths? Problem: navigational clues lost in long-range links. We’ll end up repeatedly over-shooting target. What if long-range links are uniformly random?

21. Short paths? Problem: increases path-length. We’ll end up taking forever to get anywhere. What if long-range links are very localized?

22. Decentralized search Idea: Suppose long-range links are just slightly more likely to be to close nodes. Result: Then decentralized search finds short paths.

23. Tradeoff Discovered path length Actual path length path length uniform highly local

24. Optimal tradeoff Suppose links are proportional to (1/distance)2, i.e., inverse square. Inverse square?? WTF?

25. Inverse square intuition “Scales of resolution”: Ford 3-327 2133 Sheridan Rd. Evanston, Illinois USA Room number Building Street City State Country

26. Scales of resolution Street: location within 2 miles

27. Scales of resolution City: location within 4 miles

28. Scales of resolution County: location within 8 miles

29. Scales of resolution Each new scale doubles distance from the center.

30. Scales of resolution Long-range links equally likely to connect to each different scale of resolution! (allows people to make progress towards destination no matter how far away they are)

31. How many people do you know?

32. How many people do you know?

33. How many people do you know?

34. How many people do you know?

35. How many people do you know?

36. How many people do you know?

37. How many people do you know?

38. How well did this work? For me: Neighborhood (Lakeview) 10 City (Chicago) 5 State (IL) 10 Mid-West 3 East Coast 50 United States 100 World 50

39. Inverse square in LiveJournal

40. Inverse square in LiveJournal

41. Next time decentralized search