We revisit the Random Surfer model, focusing on its--often overlooked--Teleportation component, and we introduce NCDawareRank; a novel ranking framework designed to exploit network meta-information as well as aspects of its higher-order structural organization in a way that preserves the mathematical structure and the attractive computational characteristics of PageRank. A rigorous theoretical exploration of the proposed model reveals a wealth of mathematical properties that entail tangible benefits in terms of robustness, computability, as well as modeling flexibility and expressiveness. A set of experiments on real-work networks verify the theoretically predicted properties of NCDawareRank, and showcase its effectiveness as a network centrality measure.