Auto bucle del gráfico tikzpicture que muestra la punta de la flecha en ambas direcciones

Question

tengo lo siguiente tikzpicture,

\tikzset{every picture/.style={line width=0.75pt}} 
\begin{tikzpicture}[x=0.6pt,y=0.6pt,yscale=-1,xscale=1, 
  main/.style = {draw, circle, 
  fill={rgb, 255:red, 0; green, 0; blue, 0 }},
  text=white,
  node distance=3cm,
  ->,
  >={Stealth[round,sep]}]
  \node[main] (1) {$s$};
  \node[main] (2) [right of=1]{$v_1$};
  \node[main] (3) [right of=2]{$v_2$};
  \node[main] (4) [right of=3]{$v_n$};
  \node[main] (5)[right of=4]{$t$};
  \node[text=black] at ($(3)!.5!(4)$) {\ldots};
  \draw (1) -- (2) node[midway, below, text=black]{$s_1$};
  \draw (2) -- (3) node[midway, below, text=black]{$s_1$};
  \draw (4) -- (5) node[midway, below, text=black]{$s_1$};
  \draw (2) edge[bend left] node[near start, above, text=black]{$s_0$} (1);
  \draw (3) edge[bend left] node[near start, above, text=black]{$s_0$}(1);
  \draw (4) edge[bend left] node[near start, above, text=black]{$s_0$}(1);
  \draw (1.south) edge[bend right=120, min distance=1.6cm] node[near start, below, text=black]{$s_0$} (1.north);
\end{tikzpicture}

que rinde, No estoy exactamente seguro de cómo detener la punta de la flecha que se representa en ambos lados del borde de s a s.

Cualquier ayuda es muy apreciada.