Networks: Lecture 1IntroductionA Little Bit of AnalysisStrategic InteractionsThe Road Ahead6.207/14.15: Networks Lecture 1: Introduction Daron Acemoglu and Asu Ozdaglar MIT September 9, 2009 1Networks: Lecture 1 Introduction Outline What are networks? Examples. Small worlds. Economic and social networks. “Network effects”. Networks as graphs. Strong triadic closure. Power in a network. Decisions and games in networks. Implications of strategic behavior. Rest of the course. Reading: EK, Chapter, 1 (also skim Chapters 3-5). Jackson, Chapter 1. 2Networks: Lecture 1 Introduction Introduction What are networks? Why study networks? Which networks and which commonalities? Which tools? Networks are a representation of interaction structure among units. In the case of social and economic networks, these units (nodes) are individuals or firms. At some broad level, the study of networks can encompass the study of all kinds of interactions. Information transmission. Web links. Information exchange. Trade. Credit and financial flows. Friendship. Trust. Spread of epidemics. Diffusion of ideas and innovation. 3Networks: Lecture 1 Introduction Visual Examples—1 Figure: The network structure of political blogs prior to the 2004 U.S. Presidential election reveals two natural and well-separated clusters (Adamic and Glance, 2005) Courtesy of Lada Adamic and Natalie Glance. Used with permission.Figure 1 in Adamic, Lada, and Natalie Glance. "The Political Blogosphere and the 2004 U.S. Election: Divided They Blog."In International Conference on Knowledge Discovery and Data Mining, Proceedings of the 3rd International Workshop onLink Discovery, Chicago, Illinois, 2005. New York, NY: Association for Computing Machinery (ACM), 2005,pp. 36-43. ISBN-13: 9781595932150. ISBN-10: 1595932151.4Networks: Lecture 1 Introduction Visual Examples—2 Figure: The social network of friendships within a 34-person karate club provides clues to the fault lines that eventually split the club apart (Zachary, 1977) Adapted from Figure 1 (p. 456) in Zachary, Wayne W. "An Information Flow Model forConflict and Fission in Small Groups." Journal of Anthropological Research 33, no. 4 (1977): 452-473.5Networks: Lecture 1 Introduction Visual Examples—3 Figure: The network of loans among financial institutions can be used to analyze the roles that different participants play in the financial system, and how the interactions among these roles affect the health of individual participants and the system as a whole. ( Bech and Atalay 2008) Image by MIT OpenCourseWare. Figure 9 in Bech, Morten L., and Enghin Atalay. "The Topology of theFederal Funds Market." European Central Bank Working Paper Series No. 986, December 2008. (PDF)#6Networks: Lecture 1 Introduction Visual Examples—4 Figure: The web link structure centered at http://web.mit.edu (touchgraph) 7Networks: Lecture 1 Introduction Visual Examples—5 Figure: The spread of an epidemic disease (such as the tuberculosis outbreak shown here) is another form of cascading behavior in a network. The similarities and contrasts between biological and social contagion lead to interesting research questions. (Andre et al. 2007) Courtesy of Valdis E Krebs. Used with permission.http://www.orgnet.com/contagion.html For further information, see:Andre, McKenzie, Kashef Ijaz, Jon D. Tillinghast, Valdis E. Krebs, Lois A. Diem, Beverly Metchock, Theresa Crisp, and Peter D. McElroy. "TransmissionNetwork Analysis to Complement Routine Tuberculosis Contact Investigations." American Journal of Public Health 97, no. 3 (March 2007): 470-477.8Networks: Lecture 1 Introduction Visual Examples—6 Figure: When people are influenced by the behaviors of their neighbors in the network, the adoption of a new product or innovation can cascade through the network structure. Here, e-mail recommendations for a Japanese graphic novel spread in a kind of informational or social contagion. (Leskovec et al. 2007) 9 Image by MIT OpenCourseWare. Adapted from Figure 3(b) on p. 13 in Leskovec, Jure, Lada A. Adamic, andBernardo A. Huberman. "The Dynamics of Viral Marketing." ACM Transactions on the Web 1, no. 1, Article 5(May 2007): 1-39.Networks: Lecture 1 Introduction Visual Examples—7 Figure: Percentage of total corn acreage planted with hybrid seed. (USDA Agricultural Statistics) 10Networks: Lecture 1 Introduction Do We Live in a Small World? Early 20th century Hungarian poet and writer Frigyes Karinthy first came up with the idea that we live in “small world”. He suggested, in a play, that any two people among the one and a half billion inhabitants of the earth then were linked through at most five acquaintances. The sociologist Stanley Milgram made this famous in his study “The Small World Problem” (1967)—though this study is now largely discredited. He asked certain residents of Wichita and Omaha to contact and send a folder to a target person by sending it to an acquaintance, who would then do likewise etc., until the target person was reached. This would allow Milgram to measure how many “intermediate nodes” would be necessary to link the original sender and the target. 42 of the 160 letters supposedly made it to their target, with a median number of intermediates equal to 5.5. 11Networks: Lecture 1 Introduction Do We Live in a Small World? (continued) Hence was born the idea of six degrees of separation. Can you think why Milgram’s procedure could give misleading results? Or why we may not wish to take these results on faith? There are similar studies for other types of networks. For example, Albert, Jeong, and Barabasi (1999) “Diameter of the World Wide Web” estimated that in 1998 it took on average 11 clicks to go from one random website to another (at the time there were 800 million websites). What do these kind of “small world” results imply? 12Networks: Lecture 1 Introduction Interpreting Small Worlds Suppose that each node has λ neighbors (e.g., each website has links to λ other websites). Each of my λ neighbors will then have λ neighbors themselves. Suppose (unrealistically) that my neighbors don’t have any neighbors in common (i.e., the λ websites that are linked to my website are not linked among themselves). Then in two steps, I can reach λ2 other nodes. Repeating the same reasoning (and maintaining the same unrealistic assumption), in d steps I can reach λd other nodes. Now imagine that this