Abstract. We reveal new entailments (implications) on a subset of pairwise Markov properties which hold in causal nets. The results obtained characterize a wide class of graphical models, including mixed graphs and cyclic digraphs. Three kinds of separators are defined: minimal, locally-minimal, and non-redundant. We state necessary conditions for members of non-redundant separator and propose principles of forming a non-redundant separator from elementary (in)dependency facts.

Keywords: Markov property, cyclic digraph, acyclic digraph, m-separation, non-redundant separating set, collider, identification of edges.