Social Networks

1. Social Networks

2. Lecture outline • General overview • Illustrations of types of networks • Basic concepts for thinking about networks • Implication of structural properties of networks • Triadic close & friendship formation • Structural holes & power • Small worlds & diffusion

3. What Are Social Networks? • Social network analysis – Graph-theory-based techniques for describing the topology of links between a set of people (or other objects) • Social and psychological theories – Theory about the causes and consequences of the social relationships revealed by social network analysis • Social networking sites – Internet sites based on displaying & exploiting explicit links between members e.g., Facebook, MySpace, LinkedIn, Friendster

4. Structural View • The set of (exchange) relationships between people or other social units. • A graph, with people, groups, or organizations as the nodes and the entities exchanged as the link • Vary in size, density, clumpiness • Structure matters • Clique • Isolates • Stars • Boundary spanners

5. Why are they important? • Examining social networks can help diagnose social structures: Problems & opportunities • Find most important actors • Select successful team leaders and managers • Find informational bottlenecks/distribution channels • Connected actors often influence each others’ behavior • Information flows • Flows of support • Structure is important: One’s position in a social network enables/constrains one’s options

6. Reading Structure

7. Size of personal networks Strong ties: 6-30 Weak ties: ~150 persons with interaction V. Weak ties: >1000 persons recognized Networks generally sparse Most of one’s ties don’t know each other Networks exhibit small worlds (i.e., most nodes linked via a few hops) Ties are specialized Exchange different resources with different ties (e.g., friendship & work) Only weak correlations among exchanges within a tie (e.g., correlations between communication frequency across modalities=~.3 to. 4) Strong ties useful for Money Advice Arduous help Friendship Weak ties useful for New information Dense networks are good for the group as a whole Structural holes provide opportunities for competitive advantage Balance Similar people tend to form ties Friends of friends tend to form ties Holes fill in Some Stylized Facts

8. Useful for Organizational Diagnosis

9. Race & school friendships Moody, James (2002) Race, School Integration, and Friendship Segregation in America. The American journal of sociology [0002-9602] Moody yr:2002 vol:107 iss:3 pg:679

10. 79% non-Asian 83% Asian Familiarity in a CMU Project Class

11. Links among political blogs, 2004 Adamic, L. A., & Glance, N. (2005). The political blogosphere and the 2004 US election: divided they blog LinkKDD '05 Proceedings of the 3rd international workshop on Link discovery (pp. 36-43). NY: ACM.

12. Links among political websites, 2009

13. Basic Concepts

14. Representing relations as networks

15. 1 mode: Direct links between nodes Represented by an N actor X N actor data matrix Examples Communication Advice/information Friendship Trust/social support Tangible exchange/Material support Co-authorship Similarity Links Citations “Friending” 2 mode: Indirect links between nodes joined because they participate in a common group or event Represented by N (actor) X M (group) matrix Examples Attends a common event Edits the same Wikipedia page Member of corporate board Gives to same organization Types of Edges (Relationships)

16. Directed graph (e.g, who likes whom)

17. Undirected graph (e.g, who knows whom)

18. Basic Concepts

19. Granovetter: Strength of Weak Ties • ~ 50% of new jobs come thru social contacts • Strong tie = "close relationship/friend". Social relationship with high frequency, emotional commitment, multiplicity, and reciprocity • Strong ties tend to know same things & people • Strong ties tend to fill in the gaps (e.g., friends of friends become friends; friends tend to share taste) • Weak tie = "weak relationship/causal acquaintance". Social relationships with low frequency, intensity, breadth, and reciprocity • Hypothesis: Weak ties lead to more extensive and diverse social networks, and are more likely to overcome gaps of class, race, and other sources of division • Data: Job changers get their jobs through weak ties: only 16% from contacts they see weekly and 28% from contacts they see less than yearly

20. Strength of ties on FaceBook

21. Strength of ties • Strong ties (Krackhard) • Intimacy, self-disclosure, provide support • Feel close w/frequent contact • Spouse, relatives, close friends • Weak ties (Granovetter) • Diverse resources, broader base • Feel distance w/infrequent contact • Acquaintances, colleagues from elsewhere

22. Homophily, transitivity, and bridging

23. Triadic Closure • Unconnected nodes connected to common nodes are likely to form connections • More likely to occur when their connections to the common node are strong

24. Balance theory & triadic closure(Heider, ’58; Newcomb, ’61) • Similar people form ties • Given a dyad of actors, ties tend to be reciprocated • Triadic closure: Given a triad of actors A, B and C,if A is strongly tied to B and to C, it is likely B and C will be at least weakly tied • The tendency to resolve unbalanced triads strongest when ties are affective

25. Strength of ties & likelihood of closure

26. Tie formation in an email network based on common friends • Linearity: Probability of ties formation increases with number of mutual ties already formed • Superlinearity: Having at least 2 mutual ties is especially important Kossinets, G., Kleinberg, J., & Watts, D. (2008). The structure of information pathways in a social communication network KDD '08 Proceeding of the 14th ACM SIGKDD international conference on Knowledge discovery and data mining (pp. 435-443): ACM.

27. Closure & Joining: Friendster • Linearity: Probability of ties formation increases with number of mutual ties already formed • Superlinearity: Having at least 2 mutual ties is especially important

28. Closure & Joining: Wikipedia

29. Thinking about key nodes: Degree Centrality

30. Paths and shortest paths

31. Betweenness Centrality • Betweeness coded by hue: • Reds  low betweeness centrality • Blues  high betweenness

32. Eigenvector Centrality

33. Interpreting Centrality Measures

34. Density

35. Stunning Density ComparisonHow well do you know other students in your major? Architecture BHA/BSA:

36. Who Helps Whom with the Rice Harvest? Which Village Is More Likely to Survive?

37. Clustering

38. Structural holes • A structural hole exists when there is only a weak connection between two dense clusters • Control benefits: • brokers control the interaction between two network components • Information benefits: • brokers have access to unique information, this makes them invaluable • Structural holes provide a competitive advantage • Separate non-redundant sources of information • Information from different sources is more additive than overlapping

39. Structural Holes (II)

40. Advantages of Structural Holes (Burt, 2000)

41. Small Worlds

42. Small Worlds and 6 Degrees of Separation • Small World Hypothesis: Everyone in the world can be reached through a short chain of social ties.

43. Small world phenomenon: Milgram’s& Travis(1969) experiment MA NE Instructions: Given a target individual (stockbroker in Boston), pass the message to a person you correspond with who is “closest” to the target. Travers, J., & Milgram, S. (1969). An experimental study of the small world problem. Sociometry, 32(4), 425-443.

44. MA NE Small world phenomenon:Milgram’s experiment “Six degrees of separation” Outcome: 20% of initiated chains reached target average chain length = 6.5

45. ~ 4-6 intermediaries Connections thru target’s professional circle tended to be more direct; connections thru hometown take longer.

46. Small World – Results • Common channels: • 16 (25%) reached the target through the same neighbor • 10 reached the target through one business associate, 5 through another • Nearly 50% of the letters reached the target through same three people! • “social stars” – high degree and betweenness centrality! Small World Project - Columbia University The Electronic Small World Project

47. Small World – 2002 Replication email experiment Dodds, Muhamad, Watts, Science 301, (2003) • 18 targets • 13 different countries • 60,000+ participants • 24,163 message chains • 384 reached their targets • average path length 4.0 Source: NASA, U.S. Government; http://visibleearth.nasa.gov/view_rec.php?id=2429

48. Ideal chain length btw 5 & 7 Chains more likely to complete Target & sender in same country Target & sender same gender Pass through professional ties Chains start w/in country then move to occupation Going thru hubs doesn’t help Attributions of completions • Average attrition of 63% at each link  only 384 chains complete (1.5%) • This is much larger than chance (.25%) • . • This is much worse than original Milgram (22%) Between country Number at Length L Within country Histogram of chain length by country of initial sender & target (assuming random attrition of 63%/link)

49. Watts & Strogatz (1998): Collective Dynamics of ‘Small-World’ Networks Introduced a family of “small world” networks with small diameter. Regular ‘local’ links, with some random ‘long’ links Local links ~ strong ties, provide clustering Long links ~ weak ties, provide links among clusters Intuition: Local links are like towns Long links connect the towns

50. Kleinberg (1999): The Small-World Phenomenon: An Algorithmic Perspective Considered the problem of efficient decentralized routing in small world graphs. How do people know how to efficiently get a message to someone they don’t even know? Proved that in Watts & Strogatz’s model there is no decentralized algorithm that finds short paths between nodes. Defined his own model of ‘small world’ graphs where short paths can be found in a decentralized way.