  A family of Markov blankets in a faithful Bayesian network satisfies the
symmetry and consistency properties. In this paper, we draw a bijection between
families of consistent Markov blankets and moral graphs. We define the new
concepts of weak recursive simpliciality and perfect elimination kits. We prove
that they are equivalent to graph morality. In addition, we prove that morality
can be decided in polynomial time for graphs with maximum degree less than $5$,
but the problem is NP-complete for graphs with higher maximum degrees.
