A characterization of semitwin digraphs

We introduce the class of semitwin digraphs, in which every pair of adjacent vertices u and v has N⁻(u)-\=N⁻(v)-\ N - ( u ) - { v } = N - ( v ) - { u } or N⁺(u)-\=N⁺(v)-\ N + ( u ) - { v } = N + ( v ) - { u } . We prove that every strong semitwin digraph is necessarily semicomplete, establishing a necessary structural condition in the strong case. Furthermore, we show that a connected non-strong digraph is semitwin if and only if each of its strong components is a complete digraph and its condensation digraph is isomorphic to an induced subdigraph of a member of a specific finite family of acyclic digraphs. These results provide a structural description of semitwin digraphs and clarify their relationship with well-known classes of directed graphs.