Abstract. TOPS diagrams are concise descriptions of the structural topology of proteins, and their comparison usually relies on a structural alignment of the corresponding vertex ordered and vertex and edge labelled graphs. Such an approach involves checking for the existence of subgraph isomorphisms, which is an NP complete problem even for this kind of graphs. Therefore, although there exist several algorithms for the alignment-based comparison of TOPS diagrams that are fast in practice, they have an exponential worst case complexity. Moreover, the alignment-based comparison of TOPS diagrams assumes conservation of contiguity between homologous TOPS diagram segments. In this paper, we explore the alignment-free comparison of TOPS diagrams. We consider on the one hand similarity and dissimilarity measures based on subword composition of the sequences of secondary structure elements, thus neglecting contact map information, and on the other hand the Universal Similarity Metric from Kolmogorov complexity theory. Effectiveness of these alignment-free methods for TOPS diagrams comparison is assessed by cluster validation techniques.