https://www.cs.cornell.edu/home/kleinber/link-pred.pdf
There has been extensive research on predicting links in graphs, including for social networks. For instance, David Liben-Nowell and Jon Kleinberg published a paper on this topic that would serve as a great place for more complex algorithms, linked above.
If you are going to be using graphs and networks more, going in-depth into the NetworkX package is well worth your time—the visualization options are great and the algorithms are well implemented. Another library called SNAP is also available with Python bindings, at http://snap.stanford.edu/snappy/index.html.