Definition. A (small) directed graph $G$ is a 3-tuple $(V,E,d)$ where $V$ and $E$ are sets and $d:E\to V\times V$. Similarly, a subgraph $A$ of $G$ is a 3-tuple $(V_A,E_A,d)$ such that $E_A$ is contained in $E$ and $V_A\times V_A\subseteq V\times V$ contains $d(E_A)$. Definition. If $V\times V$ is replaced with $V\times V / \{(x,y)\sim (y,x)\}$,…