Graph Properties / Features

9. Parallel edges (or multiple edges) are distinct edges that connect the same pair of vertices.
   
   In a digraph, parallel edges would be two distinct edges of the form $(v_1, v_2)$ from a vertex $v_1$ to a vertex $v_2$.
   

   There are two distinct edges connecting vertices $1$ and $2$ (and, in the digraph, $3$ and $4$,) so these are parallel edges. Miriam Briskman, CC BY-NC 4.0.

   \documentclass[border=1pt]{standalone}
   \usepackage{tikz}
   \usetikzlibrary{arrows.meta, bending}
   
   \tikzset{
   vertex/.style={draw, circle, very thick, minimum size=1cm},
   edge/.style={very thick},
   arc/.style={very thick, -Triangle},
   }
   
   \begin{document}
   
   \begin{tikzpicture}
   
   \node[vertex] (v1) at (0,0) {$1$};
   \node[vertex] (v2) at (4,0) {$2$};
   
   \draw[edge] (v1) to[bend left=25] (v2);
   \draw[edge] (v1) to[bend right=25] (v2);
   
   \draw (-0.5,-1) -- (4.5,-1);
   
   \node[vertex] (v3) at (0,-2) {$3$};
   \node[vertex] (v4) at (4,-2) {$4$};
   
   \draw[arc] (v3) to[bend left=25] (v4);
   \draw[arc] (v3) to[bend right=25] (v4);
   
   \end{tikzpicture}
   
   \end{document}