\documentclass[a4paper,12pt]{report} 

\usepackage{tikz,amsmath}

\usepackage[fleqn]{amsmath}

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

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

\begin{document}


\tikzstyle{vertex}=[circle, draw, inner sep=0pt, minimum size=3pt] 

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

\begin{tikzpicture} [scale=2,very thick]

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

\draw (0,0) .. controls (1,.5) .. (2,0);
\draw (0,0) .. controls (1,-.5) .. (2,0);

\path
(v1) edge (v2)
(v3) edge (v3)
(v2) edge (v3);

\end{tikzpicture}

\end{document}