Graph Properties / Features

5. A cycle is a closed path in which no edge is repeated and no vertex is repeated except the first and last vertex.
   

   The sequence $1,2,3,1$ forms a cycle because it starts and ends at the same vertex without repeating other vertices or edges. The sequence $1,2,3,1,2,3,1$ is a closed path but not a cycle. Miriam Briskman, CC BY-NC 4.0.

   \documentclass[border=1pt]{standalone}
   \usepackage{tikz}
   
   \tikzset{
   vertex/.style={draw, circle, very thick, minimum size=1cm},
   edge/.style={very thick}
   }
   
   \begin{document}
   
   \begin{tikzpicture}
   
   \node[vertex] (1) at (0,0) {$1$};
   \node[vertex] (2) at (3,0) {$2$};
   \node[vertex] (3) at (1.5,2) {$3$};
   
   \draw[edge] (1) -- (2);
   \draw[edge] (2) -- (3);
   \draw[edge] (3) -- (1);
   
   \end{tikzpicture}
   
   \end{document}