Special Graphs

7. A complete graph is a simple graph in which every pair of distinct vertices is connected by an edge.
   
   The complete graph on $n$ vertices is denoted by $K_n$.
   

   Every pair of vertices is connected by an edge, so this graph is the complete graph $K_4$. 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 (1.5,2.5) {$3$};
   \node[vertex] (4) at (1.5,-2.5) {$4$};
   
   \draw[edge] (1) -- (2);
   \draw[edge] (1) -- (3);
   \draw[edge] (1) -- (4);
   \draw[edge] (2) -- (3);
   \draw[edge] (2) -- (4);
   \draw[edge] (3) -- (4);
   
   \end{tikzpicture}
   
   \end{document}