Eric Gilbert and Karrie Karahalios of the University of Illinois at Urbana-Champaign have begun to study how social media can be used to predict tie strength in a sample of 2,184 Facebook relationships:
They asked 35 people to rate a number of their Facebook friends that were randomly selected. Then they looked at the Facebook behavior of these people to see if could accurate predict the strength of their ties as reported by the participants. Dimensions such as the use of words associated with intimacy and intensity, duration of communication, social distance, and other factors were looked at for their predictive power. The complete set of variables was combined to form the predictive model that worked in 85% of the instances.
Research Paper (PDF); analysis of the 74 variables used to study tie strength.