创建一个循环而不是路径

Question

如何获取一个节点，该节点有一条边循环到同一个节点，但作为一条边而不是一条路径（即没有箭头）

这是我当前的代码：

\begin{tikzpicture}
   [node distance = 20mm and 20mm,
   main/.style = {draw, circle}] 
   
   every edge quotes/.style = {auto, font=\footnotesize}
   
    \node[main] ({9})                                       {$v_1$}; 
    \node[main] ({10}) [below right of = {9}]               {$v_2$};
    \node[main] ({11}) [below of = {10}]                    {$v_3$};
    \node[main] ({13}) [below left of = {9}]                {$v_4$};
    \node[main] ({12}) [below of = {13}]                    {$v_5$};
    
    \draw ({9}) edge[""] ({10});
    \draw ({10}) edge[""] ({11});
    \draw ({11}) edge[""] ({12});
    \draw ({12}) edge[""] ({13});
    \draw ({9}) edge[""] ({13});
    \draw ({9}) edge[""] ({11});
    \draw ({9}) edge[""] ({12});
    \draw ({10}) edge[""] ({12});
    \draw ({10}) edge[""] ({13});
    \draw ({11}) edge[""] ({13});
    \draw ({1}) edge [loop above] [""] (1);

尝试制作一个在顶部顶点有循环的五面体图，但使用此代码，循环是一条路径（有一个箭头}

谢谢