> [!NOTE] Definition (Directed Graph) > A **[[Directed Graph|directed graph]]** or **digraph** is a pair of [[Sets|sets]] $(V,E)$ such that $E\subseteq V^{2}.$ The elements of $V$ are called its [[Graph vertex|vertices]] (or **nodes**, or **points**) and those of $E$ are called its **edges** which indicate a relationship between two nodes. > > [!NOTE] Definition (Directed Multigraph) > A **directed multigraph** (or **directed graph**) is a pair $(V,E)$ for some set $V$ such that $E = \{ (u_{1},u_{2} ) \mid u_{1}, u_{2} \in V \}$ is a [[Multiset|multiset]]. > # Properties