  Several classes of directed acyclic graphs have been investigated in the last
two decades, in the context of the Causal Set Program, in search for good
discrete models of spacetime. We introduce some statistical indicators that can
be used for comparing these graphs and for assessing their closeness to the
ideal Lorentzian causal sets ('causets') -- those obtained by sprinkling points
in a Lorentzian manifold. In particular, with the reversed triangular
inequality of Special Relativity in mind, we introduce 'longest/shortest path
plots', an easily implemented tool to visually detect the extent to which a
generic causet matches the wide range of path lengths between events of
Lorentzian causets. This tool can attribute some degree of 'Lorentzianity' - in
particular 'non-locality' - also to causets that are not (directly) embeddable
and that, due to some regularity in their structure, would not pass the key
test for Lorentz invariance: the absence of preferred reference frames. We
compare the discussed indicators and use them for assessing causets both of
stochastic and of deterministic, algorithmic origin, finding examples of the
latter that behave optimally w.r.t. our longest/shortest path plots.
