This paper proposes a new graph proximity measure. This measure is a derivative of network reliability. By analyzing its properties and comparing it against other proximity measures through graph examples, we demonstrate that it is more consistent with human intuition than competitors. A new deterministic algorithm is developed to approximate this measure with practical complexity. Empirical evaluation by two link prediction benchmarks, one in coauthorship networks and one in Wikipedia, shows promising results. For example, a single parameterization of the proposed measure achieves accuracies that are 14-35% above the best accuracy for each graph of all predictors reported in the 2007 Liben-Nowell and Kleinberg survey.