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\begin{figure}[htb]
  \centering
  \begin{minipage}[t]{.45\linewidth}
    \centering
   \begin{tikzpicture}[scale=2]
	% Knoten
	\node (A) at (1,2) [circle,draw] {1};
	\node (B) at (2,2) [circle,draw] {2};
	\node (D) at (2,1.25) [circle,draw] {4};
	%\node (D) at (1,1) [circle,draw] {D};
	\node (C) at (1,1.25) [circle,draw] {3};
	
	% Kanten
	\draw[->] (A) to (B);
	\draw[->] (B) to (A);
	%\draw[-] (E) to (D);
	%\draw[-] (E) to (B);
	%\draw[-] (E) to (A);
	\draw[<-] (D) to (C);
	\draw[<-] (C) to (D);
\end{tikzpicture}
    \subcaption{Test1}
  \end{minipage}%
  \hfill%
  \begin{minipage}[t]{.45\linewidth}
    \centering
    $\left( \begin{array}{rrrr}
0 & 1 & 0 & 0 \\
1 & 0 & 0 & 0 \\
0 & 0 & 0 & 1 \\
0 & 0 & 1 & 0 \\
\end{array}\right)$
    \subcaption{Test2}
  \end{minipage}
  \caption{Bildtitel}
\end{figure}

\documentclass[12pt,ngerman]{article}
\usepackage[utf8]{inputenc}
\usepackage{babel}
\usepackage{subcaption}
\usepackage{tikz}
\begin{document}
\begin{figure}[htb]
\subcaptionbox{Test1}[.5\linewidth]{\begin{tikzpicture}[node distance=1.5cm]
   % Knoten
   \node[circle,draw] (A) at (0,0)  {1};
   \node[circle,draw, right of=A] (B) {2};
   \node[circle,draw, below of=B] (D) {4};
   \node[circle,draw, below of=A] (C) {3};
   % Kanten
   \draw[<->] (A) to (B);
   \draw[<->] (C) to (D);
\end{tikzpicture}}%
\subcaptionbox{Test2}[.5\linewidth]{\centering$\left( \begin{array}{rrrr}
0 & 1 & 0 & 0 \\
1 & 0 & 0 & 0 \\
0 & 0 & 0 & 1 \\
0 & 0 & 1 & 0 \\
\end{array}\right)$}
\caption{Bildtitel}
\end{figure}
\end{document}