Theoretically, of course.
Fred Hamprecht of Heidelberg University and Germany and colleagues used data of tens of thousands of Facebook users to see if they could find out "shadow connections" of people who don't use the service:
Using the network structure of four of the university campuses, a machine-learning program picked out attributes that seemed to predict whether two non-members knew each other, such as how many members knew both of them and how many knew one but not the other. The program used only the relationships between members and the email data, both of which a social network company could access.
When the researchers then used the program to predict links between non-members in the remaining college Facebook network, 40 per cent of the predictions were correct. By contrast, they calculate that using a random guessing approach, just 2 per cent of suggested connections would be right.