They use epidemiological models to explain adoption and abandonment of social networks, where user adoption is analogous to infection and user abandonment is analogous to recovery from disease, e.g., the precipitous attrition witnessed by MySpace. To this end, they employ variants of an SIR (Susceptible Infected Removed) model to predict a precipitous decline in Facebook activity in the next few years.
Channeling Mark Twain†, FB lampooned this conclusion by pointing out that Princeton would suffer a similar demise under the same assumptions.
Irrespective of the merits of the Princeton paper, I was impressed that they used an SIR model. It's the same one I used last year to reinterpret Florence Nightingale's zymotic disease data during the Crimean War as resulting from epidemic spreading.
Another way in which FB was inadvertently dinged by incorrect interpretation of information—this time it was the math—occurred in the 2010 movie, "The Social Network" that tells the story of how FB (then called Facemash) came into being. While watching the movie, I noticed that the ranking metric that gets written on a dorm window (only in Hollywood) is wrong! The correct ranking formula is analogous to the Fermi-Dirac distribution, which is key to understanding how electrons "rank" themselves in a semiconductor.
†"The reports of my death have been greatly exaggerated."