The basic approach for predicting links is to rank all node pairs based on proximities in their graph.
Let 
denote the set of neighbors of 
in a social network.
Common neighbors [1]:
Adamic and Adar [2] refine the common neighbors by taking rarer neighbors more heavily:
Preferential attachment is based on an assumption that the probability that a new link involves node x is proportional to the number of its neighbors. The idea is famous as the growth model of the Web network [3]:
[1] Newman, M.E., Clustering and Preferential Attachment in Growing Networks, Physical Review Letters E, Vol.64(025102),2001.
[2] Adamic, L.A., E., Friends and Neighbors on the Web, Social Networks, Vol.25, No.3, pp.211-230, 2003.
[3] Getoor, L., Diehl, C.P., Link Mining: A Survey. SIGKDD Explorations, Vol.7,No.2, pp.3-12,2005.