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.

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