The feed-forward relationship naturally observed in time-dependent processes
and in a diverse number of real systems -such as some food-webs and electronic
and neural wiring- can be described in terms of so-called directed acyclic
graphs (DAGs). An important ingredient of the analysis of such networks is a
proper comparison of their observed architecture against an ensemble of
randomized graphs, thereby quantifying the {\em randomness} of the real systems
with respect to suitable null models. This approximation is particularly
relevant when the finite size and/or large connectivity of real systems make
inadequate a comparison with the predictions obtained from the so-called {\em
configuration model}. In this paper we analyze four methods of DAG
randomization as defined by the desired combination of topological invariants
(directed and undirected degree sequence and component distributions) aimed to
be preserved. A highly ordered DAG, called \textit{snake}-graph and a
Erd\:os-R\'enyi DAG were used to validate the performance of the algorithms.
Finally, three real case studies, namely, the \textit{C. elegans} cell lineage
network, a PhD student-advisor network and the Milgram's citation network were
analyzed using each randomization method. Results show how the interpretation
of degree-degree relations in DAGs respect to their randomized ensembles depend
on the topological invariants imposed. In general, real DAGs provide disordered
values, lower than the expected by chance when the directedness of the links is
not preserved in the randomization process. Conversely, if the direction of the
links is conserved throughout the randomization process, disorder indicators
are close to the obtained from the null-model ensemble, although some
deviations are observed.Comment: 13 pages, 5 figures and 5 table
