Link Prediction in Social Networks.

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.