In this work, we present an approach that utilizes a graph-based representation of symbolic musical data in the context of automatic topographic mapping. A novel approach is introduced that represents melodic progressions as graph structures providing a dissimilarity measure which complies with the invariances in the human perception of melodies. That way, music collections can be processed by non-Euclidean variants of Neural Gas or Self-Organizing Maps for clustering, classification, or topographic mapping for visualization. We demonstrate the performance of the technique on several datasets of classical music.