Given a network of known relationships between people in a social network, can we predict new or hidden relationships? There are several known methods for link prediction. For example, the Katz method counts the number of paths between people, and assigns likelihood scores based on these counts. Alternately, we can use the mathematics of electrical resistor networks, assigning scores based on resistance distance between pairs of nodes. In this talk I will describe some of the mathematics behind these link prediction algorithms. I will share some new results about computing effective resistance on certain families of graphs, and I will discuss open problems, including comparing link scoring methods on simple networks.