Special Graphs

9. A weighted graph is a graph in which edges are assigned numerical values called weights.
   
   Weights may represent distances, costs, times, or capacities.
   

   Each edge contains a numerical weight. For example, the edge between $1$ and $2$ has the weight of $5$. 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] (v1) at (0,0) {$1$};
   \node[vertex] (v2) at (4,0) {$2$};
   \node[vertex] (v3) at (2,3) {$3$};
   
   \draw[edge] (v1) -- node[above] {$5$} (v2);
   \draw[edge] (v1) -- node[left] {$2$} (v3);
   \draw[edge] (v2) -- node[right] {$7$} (v3);
   
   \end{tikzpicture}
   
   \end{document}