How does information propagate through social networks?
How can we model the information itself?
Please have a look at the Truthy project!
Do social media affect scholarly communication? Do papers that get more Twitter mentions also get more citations? Check out: Shuai X, Pepe A, Bollen J (2012) How the Scientific Community Reacts to Newly Submitted Preprints: Article Downloads, Twitter Mentions, and Citations. PLoS ONE 7(11): e47523. doi:10.1371/journal.pone.0047523
Modeling collective mood states with applications to financial market prediction: Johan Bollen, Huina Mao, and Xiao-Jun Zeng. Twitter mood predicts the stock market. Journal of Computational Science, 2(1), March 2011, Pages 1-8, doi:10.1016/j.jocs.2010.12.007, arxiv: abs/1010.3003.
Aggregating and normalizing large-scale usage data to model science in real-time. See MESUR project, and: Bollen J, Van de Sompel H, Hagberg A, Bettencourt L, Chute R, et al. (2009) Clickstream Data Yields High-Resolution Maps of Science. PLoS ONE 4(3): e4803. doi:10.1371/journal.pone.0004803