In this paper, we investigate the Normalized Semantic Web Distance (NSWD), a semantics-aware distance measure between two concepts in a knowledge graph. Our measure advances the Normalized Web Distance, a recently established distance between two textual terms, to be more semantically aware. In addition to the theoretic fundamentals of the NSWD, we investigate its properties and qualities with respect to computation and implementation. We investigate three variants of the NSWD that make use of all semantic properties of nodes in a knowledge graph. Our performance evaluation based on the Miller-Charles benchmark shows that the NSWD is able to correlate with human similarity assessments on both Freebase and DBpedia knowledge graphs with values up to 0.69. Moreover, we verified the semantic awareness of the NSWD on a set of 20 unambiguous concept-pairs. We conclude that the NSWD is a promising measure with (1) a reusable implementation across knowledge graphs, (2) sufficient correlation with human assessments, and (3) awareness of semantic differences between ambiguous concepts.