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MATH 17, Winter 2017 COMPLEX NETWORKS An Introduction to Mathematics Beyond Calculus Nishant Malik Department of Mathematics Dartmouth College February 15, 2017 Tracking Link Formation Membership Closure LiveJournal Lars Backstrom, Dan Huttenlocher, Jon Kleinberg, and Xiangyang Lan. Group formation in large social networks: Membership, growth, and evolution. In Proc. 12th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, 2006. Wikipedia David Crandall, Dan Cosley, Dan Huttenlocher, Jon Kleinberg, and Siddharth Suri. Feedback effects between similarity and social influence in online communities. In Proc. 14th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, 2008. Tracking Link Formation Membership Closure LiveJournal Lars Backstrom, Dan Huttenlocher, Jon Kleinberg, and Xiangyang Lan. Group formation in large social networks: Membership, growth, and evolution. In Proc. 12th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, 2006. Foci Link if user is in the community User User defined communities Tracking Link Formation Membership Closure LiveJournal Blogging Lars Backstrom, Dan Huttenlocher, Jon Kleinberg, and Xiangyang Lan. Group formation in large social networks: Membership, growth, and evolution. In Proc. 12th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, 2006. Foci Link if user is in the community Link b/w users if friendship is designated on the profiles User User defined communities Tracking Link Formation Membership Closure LiveJournal Blogging Lars Backstrom, Dan Huttenlocher, Jon Kleinberg, and Xiangyang Lan. Group formation in large social networks: Membership, growth, and evolution. In Proc. 12th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, 2006. Foci Link if user is in the community Membership closure User User defined communities Tracking Link Formation Membership Closure LiveJournal 4.4. TRACKING LINK FORMATION IN ON-LINE DATA 103 Lars Backstrom, Dan Huttenlocher, Jon Kleinberg, and Xiangyang Lan. Group formation in large social networks: Membership, growth, and evolution. In Proc. 12th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, 2006. Probability of joining a community when k friends are already members 0.025 0.02 probability 0.015 0.01 0.005 0 0 5 10 15 20 25 k 30 35 40 45 50 Tracking Link Formation Membership Closure Foci Link if editor has edited the article Editors Wiki Articles Wikipedia David Crandall, Dan Cosley, Dan Huttenlocher, Jon Kleinberg, and Siddharth Suri. Feedback effects between similarity and social influence in online communities. In Proc. 14th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, 2008. Tracking Link Formation Membership Closure Foci Link if editor has edited the article Link b/w editors if they have communicated (user talk page) Editors Wiki Articles Wikipedia David Crandall, Dan Cosley, Dan Huttenlocher, Jon Kleinberg, and Siddharth Suri. Feedback effects between similarity and social influence in online communities. In Proc. 14th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, 2008. Tracking Link Formation Membership Closure Foci Link if editor has edited the article Link b/w editors if they have communicated (user talk page) Editors Wiki Articles Wikipedia David Crandall, Dan Cosley, Dan Huttenlocher, Jon Kleinberg, and Siddharth Suri. Feedback effects between similarity and social influence in online communities. In Proc. 14th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, 2008. Tracking Link Formation Membership Closure Foci Link if editor has edited the article Membership closure Editors Wiki Articles Wikipedia David Crandall, Dan Cosley, Dan Huttenlocher, Jon Kleinberg, and Siddharth Suri. Feedback effects between similarity and social influence in online communities. In Proc. 14th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, 2008. Tracking Link Formation Membership Closure 104 CHAPTER 4. NETWORKS IN THEIR SURROUNDING CONTEXTS Wikipedia Figure 4.12: Quantifying the e↵ects of membership closure in a large online dataset: The plot shows the probability of editing a Wikipedia articles as a function of the number of friends who have already done [122]. David Crandall, Dan Cosley, DansoHuttenlocher, Jon Kleinberg, and Siddharth Suri. Feedback effects between similarity and social influence in online communities. In Proc. 14th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, 2008. Wikipedia article defines a focus — an editor is associated with a focus corresponding to a Quantifying the Interplay Between Selection and Social Influence Let’s get back to the old question : Origin of Homophily — Use large-scale on-line data to track processes of link formation —Wikipedia data Quantifying the Interplay Between Selection and Social Influence How do similarities in behavior between two Wikipedia editors relate to their pattern of social interaction? To answer this question we need two pieces. Measure of behavioral similarity Social network Quantifying the Interplay Between Selection and Social Influence Set of articles edited by the editor What is the behavior of an editor? ———— ———— ———— Quantifying the Interplay Between Selection and Social Influence Measure of similarity = Number of articles edited by both A & B Number of articles edited by at least one of A or B Quantifying the Interplay Between Selection and Social Influence Example Find the similarity? Editor A Editor B ——- Hanover, NH —— ———— Dartmouth ———— Cornell ———— Dartmouth Quantifying the Interplay Between Selection and Social Influence Let’s again get back to our original question Origin of Homophily In this wikipedia data we expect Homophily! * Pairs of editors who have communicated are significantly more similar in their behavior than pairs of Wikipedia editors who have not communicated Quantifying the Interplay Between Selection and Social Influence Let’s again get back to our original question Origin of Homophily In this wikipedia data we expect Homophily! The big question: *Does the Homophile arise because editors are forming connections with those who have edited the same article (SELECTION) or is it because editors are led to the articles of those they talk to (SOCIAL INFLUENCE) Quantifying the Interplay Between Selection and Social Influence Editor A Article Editor B Homophily arising because editors are forming connections with those who have edited the same articles they have (selection) Quantifying the Interplay Between Selection and Social Influence Editor A Article Already Connected Editor B Homophily arising because editors are led to the articles of those they talk to (social influence) the Interplay Between Selection and Social 6 Quantifying CHAPTER 4. NETWORKS IN THEIR SURROUNDING CONTEX Influence Social influence: continued slower increase in similarity after first contact Selection: rapid increase in similarity before first contact Quantifying the Interplay Between Selection and Social Influence Selection Editor A Similarity Editor B Social Influence