  We introduce a new method for predicting the formation of links in real-world
networks, which we refer to as the method of effective transitions. This method
relies on the theory of isospectral matrix reductions to compute the
probability of eventually transitioning from one vertex to another in a
(biased) random walk on the network. Unlike the large majority of link
prediction techniques, this method can be used to predict links in networks
that are directed or undirected which are either weighted or unweighted. We
apply this method to a number of social, technological, and natural networks
and show that it is competitive with other link predictors often outperforming
them. We also provide a method of approximating our effective transition method
and show that aside from having much lower temporal complexity, this
approximation often provides more accurate predictions than the original
effective transition method. We also, prove a number of mathematical results
regarding our effective transition algorithm and its approximation.
