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Social Networks: from Micromotives to Macrobehavior
Social Networks: from Micromotives to Macrobehavior
Social Networks: from Micromotives to Macrobehavior
Social Networks: from Micromotives to Macrobehavior
Social Networks: from Micromotives to Macrobehavior
Social Networks: from Micromotives to Macrobehavior
Social Networks: from Micromotives to Macrobehavior
Social Networks: from Micromotives to Macrobehavior
Social Networks: from Micromotives to Macrobehavior
Social Networks: from Micromotives to Macrobehavior
Social Networks: from Micromotives to Macrobehavior
Social Networks: from Micromotives to Macrobehavior
Social Networks: from Micromotives to Macrobehavior
Social Networks: from Micromotives to Macrobehavior
Social Networks: from Micromotives to Macrobehavior
Social Networks: from Micromotives to Macrobehavior
Social Networks: from Micromotives to Macrobehavior
Social Networks: from Micromotives to Macrobehavior
Social Networks: from Micromotives to Macrobehavior
Social Networks: from Micromotives to Macrobehavior
Social Networks: from Micromotives to Macrobehavior
Social Networks: from Micromotives to Macrobehavior
Social Networks: from Micromotives to Macrobehavior
Social Networks: from Micromotives to Macrobehavior
Social Networks: from Micromotives to Macrobehavior
Social Networks: from Micromotives to Macrobehavior
Social Networks: from Micromotives to Macrobehavior
Social Networks: from Micromotives to Macrobehavior
Social Networks: from Micromotives to Macrobehavior
Social Networks: from Micromotives to Macrobehavior
Social Networks: from Micromotives to Macrobehavior
Social Networks: from Micromotives to Macrobehavior
Social Networks: from Micromotives to Macrobehavior
Social Networks: from Micromotives to Macrobehavior
Social Networks: from Micromotives to Macrobehavior
Social Networks: from Micromotives to Macrobehavior
Social Networks: from Micromotives to Macrobehavior
Social Networks: from Micromotives to Macrobehavior
Social Networks: from Micromotives to Macrobehavior
Social Networks: from Micromotives to Macrobehavior
Social Networks: from Micromotives to Macrobehavior
Social Networks: from Micromotives to Macrobehavior
Social Networks: from Micromotives to Macrobehavior
Social Networks: from Micromotives to Macrobehavior
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Social Networks: from Micromotives to Macrobehavior

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  • 1. Social Networks: from Micromotives to Macrobehavior Leonid Zhukov Moscow, June 2014
  • 2. http://bks5.books.google.ru/books? id=AOsWGCuRDhkC&printsec=frontcover&img=1&zoom=1&im gtk=AFLRE71eJXO_WkVQX1OwrD8c5jzrap6PMfFt6GPTfvFv7y WTB- vvK8lOlA9ZxSCE39_Fr1KvgDuwmCxWJqyMirnJe4Bh4K1NNeE RlH3ei49yR4inV085FAPrsEl9V763tRfqakMvrJHu Micromotives and macrobehavior Combined local actions -> global results Simple rules -> complex behavior Local structure -> global properties Thomas C. Shelling, 1978! Nobel Prize in Economics 2005
  • 3. Talk outline Network structure Network models Processes on networks
  • 4. Complex networks: social networks, internet, WWW, citation networks, financial networks, trade networks, transportation networks, protein interaction networks, brain networks, food web, language networks, …
  • 5. Network structure
  • 6. Local structure Node degree = # of friends
  • 7. Global: degree distribution How many people with: 1 friend 2 friends 3 friends ! Distribution: P(n) Power-law distribution
  • 8. Power-law degree distribution
  • 9. Local structure Node degree = # of friends! Friend’s friends = triangles
  • 10. http://bks5.books.google.ru/books? id=AOsWGCuRDhkC&printsec=frontcover&img=1&zoom=1&im gtk=AFLRE71eJXO_WkVQX1OwrD8c5jzrap6PMfFt6GPTfvFv7y WTB- vvK8lOlA9ZxSCE39_Fr1KvgDuwmCxWJqyMirnJe4Bh4K1NNeE RlH3ei49yR4inV085FAPrsEl9V763tRfqakMvrJHu The strength of weak “The Strength of Weak Ties”. Mark Granovetter. 1973 Mark Granovetter. The strengtth of weak ties , American Journal of Sociology, 78(6):1360-1380, 1973
  • 11. Triadic closer Strength of ties Triadic closure: if A and B and A and C are strongly linked, then the tie between B and C is always present Clustering coefficient
  • 12. Global: community structure
  • 13. Local structure Node degree = # of friends! Friend’s friends = triangles! “Long connections” = small network diameter
  • 14. http://bks5.books.google.ru/books? id=AOsWGCuRDhkC&printsec=frontcover&img=1&zoom=1&im gtk=AFLRE71eJXO_WkVQX1OwrD8c5jzrap6PMfFt6GPTfvFv7y WTB- vvK8lOlA9ZxSCE39_Fr1KvgDuwmCxWJqyMirnJe4Bh4K1NNeE RlH3ei49yR4inV085FAPrsEl9V763tRfqakMvrJHu Small world J. Travers and S. Milgram. An Experimental Study of the Small World Problem. Sociometry, vol 32, No 4, pp 425-433, 1969
  • 15. http://bks5.books.google.ru/books? id=AOsWGCuRDhkC&printsec=frontcover&img=1&zoom=1&im gtk=AFLRE71eJXO_WkVQX1OwrD8c5jzrap6PMfFt6GPTfvFv7y WTB- vvK8lOlA9ZxSCE39_Fr1KvgDuwmCxWJqyMirnJe4Bh4K1NNeE RlH3ei49yR4inV085FAPrsEl9V763tRfqakMvrJHu 1969 Experiment 296 volunteers, 217 sent 196 Nebraska (1300 miles) 100 Boston (25 miles) target in Boston vaguely ‘out there,’ on the Great Plains or somewhere.” There was little consensus about how many links it would take to connect people from these remote areas. Milgram himself pointed out in 1969, “Recently I asked a person of intelligence how many steps he thought it would take, and he said that it would require 100 intermediate persons, or more, to move from Nebraska to Sharon.” Milgram’s experiment entailed sending letters to randomly chosen residents of Wichita and Omaha asking them to participate in a study of social contact in American society. The letter contained a short summary of the study’s purpose, a photograph, and the name and ad- dress of and other information about one of the target persons, along with the following four-step instructions: HOW TO TAKE PART IN THIS STUDY 1. ADD YOUR NAME TO THE ROSTER AT THE BOT- TOM OF THIS SHEET, so that the next person who re- ceives this letter will know who it came from. 2. DETACH ONE POSTCARD. FILL IT OUT AND RE- TURN IT TO HARVARD UNIVERSITY. No stamp is needed. The postcard is very important. It allows us to keep track of the progress of the folder as it moves toward the tar- get person. 3. IF YOU KNOW THE TARGET PERSON ON A PER- SONAL BASIS, MAIL THIS FOLDER DIRECTLY TO HIM (HER). Do this only if you have previously met the target person and know each other on a first name basis. 4. IF YOU DO NOT KNOW THE TARGET PERSON ON A PERSONAL BASIS, DO NOT TRY TO CONTACT HIM DIRECTLY. INSTEAD, MAIL THIS FOLDER (POST- CARDS AND ALL) TO A PERSONAL ACQUAIN- TANCE WHO IS MORE LIKELY THAN YOU TO KNOW THE TARGET PERSON. You may send the folder to a friend, relative or acquaintance, but it must be someone you know on a first name basis. Milgram had a pressing concern: Would any of the letters make it to the target? If the number of links was indeed around one hundred, as his friend guessed, then the experiment would likely fail, since there is always someone along such a long chain who does not cooperate. It was therefore a pleasant surprise when within a few days the first letter ar- rived, passing through only two intermediate links! This would turn out to be the shortest path ever recorded, but eventually 42 of the 160 let- ters made it back, some requiring close to a dozen intermediates. These completed chains allowed Milgram to determine the number of people Six Degrees of Separation 29 0738206679-01.qxd 3/13/02 2:08 PM Page 29 NAME, ADDRESS, OCCUPATION, JOB, HOMETOWN
  • 16. 1969 Experiment reached the target N = 64, 29% ave chain length <l> = 5.2 channels: hometown <l> = 6.1 business contacts <l> = 4.6 Location: boston <l> = 4.4 nebraska <l> = 5.7
  • 17. 1994,Premiere magazine Six degrees of Kevin Bacon
  • 18. Universal properties of social networks Power low degree distribution Large clustering coefficient Small world effect ! Gigantic connected component Tight core and periphery Hierarchical structure
  • 19. Network models
  • 20. Small world network Duncan J. Watts and Steven H. Strogatz. Collective dynamics of ‘small-world’ networks. . Nature 393:440-42, 1998.
  • 21. Preferential attachment
  • 22. Preferential attachement AL Barabasi and R. Albert. Emergence of Scaling in Random Networks. Science, 286, 1999.
  • 23. Strategic network formation Utility function Distance based utility Costs and benefits of connections Maximizing individual utility Matthew O. Jackson, Asher Wolinsky, . A Strategic Model of Social and Economic Networks. Journal of Economic Theory, Vol 71, pp 44-74, 1996. 50 CHAPTER 2. REPRESENTING AND MEASURING NETWORKS
  • 24. http://bks5.books.google.ru/books? id=AOsWGCuRDhkC&printsec=frontcover&img=1&zoom=1&im gtk=AFLRE71eJXO_WkVQX1OwrD8c5jzrap6PMfFt6GPTfvFv7y WTB- vvK8lOlA9ZxSCE39_Fr1KvgDuwmCxWJqyMirnJe4Bh4K1NNeE RlH3ei49yR4inV085FAPrsEl9V763tRfqakMvrJHu Strategic network formation Pairwise stable small world network224 CHAPTER 6. STRATEGIC NETWORK FORMATION Figure 6.5.1. A Pairwise Stable ìSmall Worldî in an Islands Version of the Connections Model The intuition behind the proposition is relatively straightforward. Low costs of connections to nearby players (those on the same island) lead to high clustering. The
  • 25. Processes on networks
  • 26. Processes on networks Information propagation diffusive virus like Decision making threshold models
  • 27. Diffusion model method - diffusion virus model “infected” on contact probability depends on immunity  can model news gossips
  • 28. Diffusion model Step 1
  • 29. Diffusion model Step 2
  • 30. Diffusion model Step 3
  • 31. Diffusion model Step 4
  • 32. Diffusion model Step 5 ! Complete coverage Process time depends on the source Based on connectivity pattern
  • 33. Twitter retweet mention “Truthy” Project. Center for Complex Networks and System Research. Indiana University. #newsjp #iraq #ocra
  • 34. Threshold model neighbors “opinion” decision threshold information cascade model: beliefs propagation purchasing decisions spread of innovations A,B - types of behavior q –decision threshold If fraction of neighbors with A greater than q, accpet A
  • 35. Threshold model threshold= 1/2
  • 36. Threshold model Step 1 2 sources threshold= 2/5
  • 37. Threshold model Step 2
  • 38. Threshold model Step 3 !
  • 39. Threshold model Step 4 incomplete cascade depends on network topology strongly depends on source selection
  • 40. Cascade maximization Cascade maximization problem Strategic source placement Well connected group of nodes Inside various communities Increase of competitive advantage reduce threshold level
  • 41. Visual Complexity www.visualcomplexity.com
  • 42. http://bks5.books.google.ru/books? id=AOsWGCuRDhkC&printsec=frontcover&img=1&zoom=1&im gtk=AFLRE71eJXO_WkVQX1OwrD8c5jzrap6PMfFt6GPTfvFv7y WTB- vvK8lOlA9ZxSCE39_Fr1KvgDuwmCxWJqyMirnJe4Bh4K1NNeE RlH3ei49yR4inV085FAPrsEl9V763tRfqakMvrJHu Textbooks
  • 43. http://bks5.books.google.ru/books? id=AOsWGCuRDhkC&printsec=frontcover&img=1&zoom=1&im gtk=AFLRE71eJXO_WkVQX1OwrD8c5jzrap6PMfFt6GPTfvFv7y WTB- vvK8lOlA9ZxSCE39_Fr1KvgDuwmCxWJqyMirnJe4Bh4K1NNeE RlH3ei49yR4inV085FAPrsEl9V763tRfqakMvrJHu Easy read

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