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Reading Group “Networks, Crowds and Markets”

Typ hier de naam van de FEB afzender. Reading Group “Networks, Crowds and Markets”. Session 1: Graph Theory and Social Networks. Overview. Introduction Reading Group Ch. 2 Graphs, Paths and Small Worlds Ch. 3 Strength of Weak Ties Ch. 4 Homophily Schelling model.

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Reading Group “Networks, Crowds and Markets”

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  1. Typ hier de naam van de FEB afzender Reading Group “Networks, Crowds and Markets” Session 1: Graph Theory and Social Networks

  2. Overview • Introduction Reading Group • Ch. 2 Graphs, Paths and Small Worlds • Ch. 3 Strength of Weak Ties • Ch. 4 Homophily • Schelling model Typ hier de footer

  3. Introduction to the Reading Group • Book: Networks, Crowds and Markets • Why this book? • Multidisciplinary and Comprehensive • Networks: Jon Kleinberg, Computer Scientist • Crowds and Markets: David Easley: Economist • Up to date (2010) • Good Reputation Typ hier de footer

  4. Introduction to the Reading Group • Additional comments • Treated chapters are in Syllabus • Chapters are online: • http://www.cs.cornell.edu/home/kleinber/networks-book/ • Book is at Undergraduate level • Consider Advanced Material and additional papers when presenting Typ hier de footer

  5. Chapter 2 GRAPHS, PATHS AND SMALL WORLDS Typ hier de footer

  6. A social network Typ hier de footer

  7. A financial network Typ hier de footer

  8. A technological network: ARPANET Typ hier de footer

  9. Graphs, Paths and Distances • A network is mathematically represented by a graph, G=<V,E>, a set of vertices (nodes) V and the edges (ties, links) between them • A graph can be directed or undirected Typ hier de footer

  10. Graphs, Paths and Distances • A path is a sequence of (distinct) nodes, v1, v2, …, vk, such that for each i in {1,…,k-1} there is an edge between vi and vi+1 GJHML is a path Typ hier de footer

  11. Graphs, Paths and Distances • The distance between two nodes v1 and v2 is the length of the shortest path between them The shortest path between G and L is (among others) GJHL and its length is 3 Typ hier de footer

  12. Small-World Phenomenon • When we look at large social network with thousands of nodes, we find that distances are generally quite short, often less than 10. This is called the Small-World phenomenon • Stanley Milgram e.a. in 1960s: Small World Experiment • Random participants in Nebraska and Kansas were asked to send a chain letter to Boston through first-name based acquaintances Typ hier de footer

  13. Distribution of Chain Lengths Typ hier de footer

  14. Small Worlds • Milgram found that average lengths of the chains in the experiment was around six • Six degrees of separation • This number has been replicated in other studies, e.g. Leskovec & Horvitz in Microsoft Instant Messenger network • Why is this? Typ hier de footer

  15. Small-World Phenomenon • Suppose everyone has on average 100 acquaintances and there is little overlap between acquaintanceships • Me: 1 • Acquaintances: 100 • Acquaintances at distance 2: 100^2=10,000 • Acquaintances at distance 3: 100^3=1,000,000 • Acquaintances at distance 4: 100^4=100,000,000 • Acquaintances at distance 5: 100^5=10,000,000,000 Typ hier de footer

  16. Chapter 3 STRENGTH OF WEAK TIES Typ hier de footer

  17. Strength of Weak Ties • Links differ in terms of strength • Friends vs. Acquaintance • Amount of contact time, affection, trust • Mark Granovetter (1974): Getting a Job • Jobseekers obtain useful job info through social network • More often from acquaintances than from close friends • Why? Typ hier de footer

  18. Strength of Weak Ties • Granovetter (1973): The Strength of Weak Ties • Link between local network property and global network structure • Local: Triadic closure of triads with strong ties • Local-Global: Strong ties cannot be bridges • Global: Bridges more important for information transmission • Conclusion: Weak ties are more important for information transmission Typ hier de footer

  19. Strength of Weak Ties • Triadic closure of triads with strong ties • A satisfies strong triadic closure property: • for all B and C for which there is a strong tie AB and AC, there is also a (strong or weak) tie BC B B A A C C Typ hier de footer

  20. Strength of Weak Ties • A bridge is a tie that connects two otherwise unconnected components • Information within group is often same • Information between groups is different • Bridge provides link to different information source, and is therefore more important E B C D A F Typ hier de footer

  21. Strength of Weak Ties • Tie AB is a local bridge if A and B have no friends in common • The span of a local bridge AB is the distance between A and B after removal of AB itself AB is a local bridge of span 4 B A Typ hier de footer

  22. Strength of Weak Ties • Claim: if a node A satisfies the Strong Triadic Closure and is involved in at least two strong ties, then any local bridge it is involved in must be a weak tie • Proof by contradiction: suppose C satisfies STC and CD is a strong bridge, then there is a triple BCD with BC and CD strong. But then, BD should be linked. E B C D F A Typ hier de footer

  23. Strength of Weak Ties • Empirical support for Strength of Weak Ties Theory • Onnela et al. (2007) • Empirical support against Strength of Weak Ties Theory • Van der Leij & Goyal (2011) Typ hier de footer

  24. Chapter 4 HOMOPHILY Typ hier de footer

  25. Homophily • Agents in a social network have other characteristics apart from their links • Non-mutable: race, gender, age • Mutable: place to live, occupation, activities, opinions, beliefs • Links and mutable characteristics co-evolve over time Typ hier de footer

  26. Homophily • When we take a snapshot in time, we observe that these node characteristics are correlated across links • E.g. Academics have often academic friends, etc. • This phenomenon that people are linked to similar others is called homophily Typ hier de footer

  27. Homophily at a U.S. High School Typ hier de footer

  28. Homophily • Mechanisms underlying Homophily • Selection • A and B have similar characteristics -> A and B form a link AB • Social Influence • A and B have a link -> B chooses the same (mutable) characteristic as A • E.g. A starts smoking, and B follows (peer pressure) Typ hier de footer

  29. Social-Affiliation Network • Network of persons and social foci (activities) Typ hier de footer

  30. Triadic Closure Typ hier de footer

  31. Focal Closure • Selection: Karate introduces Anna to Daniel Typ hier de footer

  32. Membership Closure • Social Influence: Anna introduces Bob to Karate Typ hier de footer

  33. Homophily • Both Selection and Social Influence drive homophily • How important is each mechanism? • Important question: Different mechanism implies different policy, • e.g. Policy to prevent teenagers from smoking • Social Influence. Target “key players” and let them positively influence rest • Selection. Target on characteristics (e.g. family background) alone Typ hier de footer

  34. Homophily • Both Selection and Social Influence drive homophily • How important is each mechanism? • Difficult question: • Requires longitudinal data • Requires observation of (almost) all characteristics • If a characteristic is not observed, then social influence effect is overestimated Typ hier de footer

  35. Homophily • Measuring the mechanisms behind homophily is a hot topic • Kossinets & Watts (2006): Detailed course and e-mail interaction data from university • Centola (2010, 2011): Experimental data on social influence controlling network structure • Sacerdote: Social influence among students after randomized dorm assignment Typ hier de footer

  36. Homophily and Segregation • Neighborhoods tend to be segregated according to race or culture • Ghetto formation • What is the mechanism behind that? Typ hier de footer

  37. Segregation in Chicago Typ hier de footer

  38. Homophily and Segregation • Segregation model of Thomas Schelling • Agent-based model • Two different agents: X and O types • Agents live on a grid • weak satisficing preferences for homophily • At least k of the 8 neighbors of same type • Each period, agents who are not satisfied move to a location where they are Typ hier de footer

  39. Schelling’s model (k=3) X Typ hier de footer

  40. Schelling’s model (k=3) X Typ hier de footer

  41. Schelling’s model online • http://cs.gmu.edu/~eclab/projects/mason/projects/schelling/ Typ hier de footer

  42. Typ hier de footer

  43. Schelling’s model • Surprising relation between micro-behavior and macro-outcomes • Weak satisficing preferences for homophily sufficient to create complete segregation • Segregation arises due to miscoordination • There exists an allocation involving complete integration satisfying all agents, but individual decisionmaking does not lead to that outcome Typ hier de footer

  44. Overview • Introduction Reading Group • Ch. 2 Graphs, Paths and Small Worlds • Ch. 3 Strength of Weak Ties • Ch. 4 Homophily • Schelling model • Planning • Next week: 6 March 13:00 • Natasa Golo and Dan Braha • Next Reading Group: 13 March 13:30 h • Maurice Koster: Ch. 8 and Ch. 10 Typ hier de footer

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