\documentclass{article} 

\usepackage{tikz,amsmath}

\begin{document}

\tikzstyle{vertex}=[circle, draw, inner sep=0pt, minimum size=5pt] 

\newcommand{\vertex}{\node[vertex]}

\begin{tikzpicture} [scale=5,very thick]

\vertex[fill] (v1) at (0,0) [label=left:$v_{1}$] {};
\vertex[fill] (v2) at (1,0) [label=right:$v_{2}$] {};
\vertex[fill] (v3) at (.5,-1) [label=right:$v_{3}$] {};

\draw (0,0) .. controls (1,1) .. (1,0);
\draw (1,0) .. controls (.5,-1) .. (.5,-1);
\draw[-] (.5,-1) .. controls (.1,-1) and (.5,-.8) .. (.5,-1); 

\path
(v1) edge (v2)


(v2) edge (v3);

\end{tikzpicture}

\end{document}