  Dual graphs have been applied to model RNA secondary structures with
pseudoknots, or intertwined base pairs. In previous works, a linear-time
algorithm was introduced to partition dual graphs into maximally connected
components called blocks and determine whether each block contains a pseudoknot
or not. As pseudoknots can not be contained into two different blocks, this
characterization allow us to efficiently isolate smaller RNA fragments and
classify them as pseudoknotted or pseudoknot-free regions, while keeping these
sub-structures intact. Moreover we have extended the partitioning algorithm by
classifying a pseudoknot as either recursive or non-recursive in order to
continue with our research in the development of a library of building blocks
for RNA design by fragment assembly. In this paper we present a methodology
that uses our previous results and classify pseudoknots into the classical
H,K,L, and M types, based upon a novel representation of RNA secondary
structures as dual directed graphs (i.e., digraphs). This classification would
help the systematic analysis of RNA structure and prediction as for example the
implementation of more accurate folding algorithms.
