  We propose custom made cell complexes, in particular prodsimplicial
complexes, in order to analyze data consisting of directed graphs. These are
constructed by attaching cells that are products of simplices and are suited to
study data of acyclic directed graphs, called here consistently directed
graphs. We investigate possible values of the first and second Betti numbers
and the types of cycles that generate nontrivial homology. We apply these tools
to directed graphs associated with reductions of double occurrence words, words
that are associated with DNA recombination processes in certain species of
ciliates. We study the effects of word operations on the homology for these
graphs.
