  Directed acyclic graph (DAG) models are popular for capturing causal
relationships. From observational and interventional data, a DAG model can only
be determined up to its \emph{interventional Markov equivalence class} (I-MEC).
We investigate the size of MECs for random DAG models generated by uniformly
sampling and ordering an Erd\H{o}s-R\'{e}nyi graph. For constant density, we
show that the expected $\log$ observational MEC size asymptotically (in the
number of vertices) approaches a constant. We characterize I-MEC size in a
similar fashion in the above settings with high precision. We show that the
asymptotic expected number of interventions required to fully identify a DAG is
a constant. These results are obtained by exploiting Meek rules and coupling
arguments to provide sharp upper and lower bounds on the asymptotic quantities,
which are then calculated numerically up to high precision. Our results have
important consequences for experimental design of interventions and the
development of algorithms for causal inference.
