**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.