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Andre et al 2007 courtesy of valdis e krebs used with

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Unformatted text preview: d 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. "Transmission Network Analysis to Complement Routine Tuberculosis Contact Investigations." American Journal of Public Health 97, no. 3 (March 2007): 470-477. Networks: Lecture 1 Introduction Visual Examples—6 Image by MIT OpenCourseWare. Adapted from Figure 3(b) on p. 13 in Leskovec, Jure, Lada A. Adamic, and Bernardo A. Huberman. "The Dynamics of Viral Marketing." ACM Transactions on the Web 1, no. 1, Article 5 (May 2007): 1-39. 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 Networks: Lecture 1 Introduction Visual Examples—7 Figure: Percentage of total corn acreage planted with hybrid seed. (USDA Agricultural Statistics) 10 Networks: 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. 11 Networks: 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? 12 Networks: 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...
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