CSCI 2350/INTD 2350: Social & Economic Networks What does a - PDF document

2/2/15 ¡ CSCI 2350/INTD 2350: Social & Economic Networks What does a real-world network look like? Reading: Ch 2 of EK, Ch 2 & 3 of Jackson Mohammad T . Irfan Email: mirfan@bowdoin.edu Networks and contagion u Ebola epidemic December 2013 – present 1 ¡

2/2/15 ¡ Real-World Networks And their common properties 1. Macro-level 2. Micro-level Macro-level properties 1. Giant components 2. Small-world effect 3. Degree distribution 4. Clustering 2 ¡

2/2/15 ¡ 1. Giant component u Intuitive example u Actor network u 98% of 449,913 actors belong to the giant component (May 2000) u Other examples u Instant messaging u Co-author network u Email u Biological networks (neural networks) u Technology networks (WWW, power grid) What is the implication? High school relationships (1993-95) 3 ¡

2/2/15 ¡ 2. Small-world effect u Proposition u The average shortest path between any two nodes in a connected component is “small” u Intuition Six degrees of separation u Hungarian author Frigyes Karinthy (1929 short story “Chains”) u John Guare’s play (1990) & later movie 4 ¡

2/2/15 ¡ Milgram’s experiment (1963) Milgram’s experiment (cont…) u Critiques… 5 ¡

2/2/15 ¡ What is the implication of small-world? “Six worlds apart?” Contagion of TB (Valdis Krebs, Oklahoma, 2002) 6 ¡

2/2/15 ¡ Computational question u How to find the “right 6 people?” u Breadth-first search (BFS) algorithm to find the shortest path u Fun application– Bacon number u Bacon number of an actor = distance from Kevin Bacon u Average Bacon number: 2.9 u https://oracleofbacon.org/ Patrick Dial M for Murder Allen Grace Kelly High Noon The Eagle Has Landed Nicole Cold Mountain Lloyd Kidman Bridges Donald Sutherland Kathleen Joe vs. Volcano Quinlan Animal House John Tom Kevin Apollo 13 Belushi Hanks Bacon Da Vinci Yves Code Bill Portrait of a Lady Aubert The Wild River Paxton Paul Meryl Titanic Herbert Streep Kate John Holiday Winslet Gielgud Hamlet Cameron Diaz Bill Charlie’s Angels Murray 7 ¡

2/2/15 ¡ 3. Degree distribution u Power law distribution and scale-free networks 4. Clustering coefficients u Highly clustered 8 ¡

2/2/15 ¡ Political blogs (2004) Micro-level properties u Centrality u Controversial topic u 4 types 9 ¡

2/2/15 ¡ Centrality measures Degree centrality 1. Closeness centrality 2. Betweenness centrality 3. Prestige/eigenvector centrality 4. Review: Closeness centrality u Centrality of node i = 1/average shortest path length from i to all other nodes u Q: How to compute closeness centrality? 10 ¡

2/2/15 ¡ Centrality measures Degree centrality 1. Closeness centrality 2. Betweenness centrality 3. Prestige/eigenvector centrality 4. Eigenvector centrality u Tutorial on eigenvector u Jackson’s Section 2.4 (Appendix) u http://www.mathportal.org/calculators/matrices- calculators/matrix-calculator.php 11 ¡

2/2/15 ¡ Comparison of centrality measures 12 ¡