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

Betti Numbers of Prodsimplicial Complexes for Directed Graphs with Applications to Word Reductions