This paper presents a new semantic relatedness measure on semantic networks (SN) that uses both hierarchical and non-hierarchical relations. Our approach relies on two assumptions. Firstly, in a given SN, only a few numbers of paths can be considered as “semantically correct” and these paths obey to a given set of rules. Secondly, following a given edge in a path has a cost (which depends on its type, is-a, part-of, etc.) and its position in the path. We propose an evaluation of our measure on WordNet with two different benchmarks, using the part-of relation. We show that, in this context, our measure does better than the classical semantic measures.