Special Graphs

6. A graph is called regular if all vertices have the same degrees.
   
   If every vertex has degree $k$, the graph is called a $k$-regular graph.
   

   The degree of every node in this graph is $2$: this is a $2$-regular graph. 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 (3,-3) {$3$};
   \node[vertex] (4) at (0,-3) {$4$};
   
   \draw[edge] (1) -- (2);
   \draw[edge] (2) -- (3);
   \draw[edge] (3) -- (4);
   \draw[edge] (4) -- (1);
   
   \end{tikzpicture}
   
   \end{document}