1 / 44

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.

aneko
Télécharger la présentation

Reading Group “Networks, Crowds and Markets”

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  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

More Related