\documentclass[12pt, reqno]{amsart}
\usepackage{amsmath, amsthm, amscd, amsfonts, amssymb, graphicx, color}
\usepackage[bookmarksnumbered, colorlinks, plainpages]{hyperref}
\usepackage{tikz}
\usepackage{amssymb}
\usepackage[utf8]{inputenc}
\usepackage[upright]{fourier}
\usepackage{tkz-graph}
\usepackage[labelsep=quad,indention=7pt]{caption}
\usepackage{subfigure}

\begin{document}
\begin{figure}[!h]
\begin{minipage}[b]{.5\linewidth}
\centering  $G_1~~~~$
\begin{tikzpicture}[scale=.6, transform shape]
\SetGraphUnit{2}
\GraphInit[vstyle=Classic]
\Vertex[Lpos=-90]{A}
\EA[Lpos=-90](A){B}
\NO[Lpos=0](B){C}
\NO[Lpos=0](A){D}
\Edge [style={thick, ->},
color=black](A)(B)
\Edge [style={thick, ->},
color=black](B)(C)
\Edge [style={bend right, thick, <- },
color=black](C)(A)
\Edge [style={thick, ->},
color=black](D)(B)
\end{tikzpicture}
\end{minipage}%
\begin{minipage}[b]{.5\linewidth}
\centering $G_2~~~~$
\begin{tikzpicture}[scale=.6, transform shape]
\SetGraphUnit{2}
\GraphInit[vstyle=Classic]
\Vertex[Lpos=-90]{A}
\EA[Lpos=-90](A){B}
\NO[Lpos=0](B){C}
\NO[Lpos=0](A){D}
\Edge [style={thick, <-},
color=black](A)(B)
\Edge [style={thick, <-},
color=black](B)(C)
\Edge [style={bend right, thick, ->},
color=black](C)(A)
\Edge [style={thick, <-},
color=black](D)(B)
\end{tikzpicture}
\end{minipage}%
\end{figure}

\end{document}