Given any digraphs $G$ and $H$ we say a surjection $f:V(G)\to V(H)$ reduces $G$ to $H$ if and only if it satisfies $(u,v)\in E(G)\iff (f(u),f(v))\in E(H)$. Where if there exists at least one surjection that reduces $G$ to $H$ then we refer to $H$ as a reduction of $G$ and write $H\preceq G$. Thus by this definition we see $\preceq$ forms a pre-order and in fact a partial order with respect to isomorphism classes of digraphs as $\small(G\preceq H)\land (H\preceq G)\implies G\cong H$. Lastly we call any digraph $D$ irreducible if and only if every reduction of $D$ is isomorphic to $D$.

With that said does every finite digraph have a unique (up to isomorphism) irreducible reduction?