Small world, Clustering, and Weak ties

Required readings

• S. Milgram, The Small-World Problem, Pscyhology today, 1967.
• P.S. Dodds et al., An Experimental Study of Search in Global Social Networks, Science, 2003.
• M.S. Granovetter, The Strength of Weak Ties, American Journal of Sociology, 1973.
• D.J. Watts and S.H. Strogatz, Collective Dynamics of 'Small-World' Networks, Nature, 1998.

Recommended readings

• J. Travers and S. Milgram, An Experimental Study of the Small World Problem, Sociometry, 1969
• L. Backstrom et al., Four Degrees of Separation, arXiv, 2011.
• J.P. Onnela et al., Structure and tie strengths in mobile communication networks, PNAS, 2007.
• Barabási, Ch. 2
• Easley & Kleinberg, Ch. 3
• Easley & Kleinberg, Ch. 20
• Aaron Clauset, Lecture note 1-2

Further readings

• J. Leskovec and E. Horvitz, Planetary-scale views on a large instant-messaging network, WWW'08
• C.R. Palmer et al., ANF: A fast and scalable tool for data mining in massive graphs, KDD'02.

Questions

1. Describe what is the small-world phenomenon.
2. What are the two views on the structure of social networks that Milgram suggested?
3. Under what kinds of assumptions the small-world phenomenon is surprising? One regarding the density of social networks and other regarding the 'in-breeding' of social contacts.
4. What were the common search strategies in the email study?
5. What is 'funneling' described by Milgram?
6. What are the Granovetter's assumptions about the position of strong ties and weak ties?

Questions for discussion

• Is small-world phenomenon strange? why or why not?
• If you want to test the hypothesis that there's small-world phenomenon, how will you design the experiment? Is there any caveats of the existing experiment designs?
• How can one test the weak-tie hypothesis?
• Can you think of other ways to model a network with both high clustering and short path length?