I already draw the directed graph but it shows some error. MWE:
\begin{document}
\begin{figure}
\begin{tikzpicture}[>=stealth',shorten >=1pt,node distance=3cm,%
on grid,initial/.style ={}]
\node[state] (T1) {$T1$};
\node[state] (T2) [below left=of T1] {$T2$};
\node[state] (T3) [below left=of T1] {$T3$};
\node[state] (T4) [below right=of T1] {$T1$};
\node[state] (T5) [below right=of T1] {$T5$};
\node[state] (T6) [below right=of T1] {$T6$};
\node[state] (T8) [below right=of T2] {$T8$};
\node[state] (T9) [below left=of T2] {$T9$};
\node[state] (T7) [below left=of T3] {$T7$};
\node[state] (T8) [below left=of T4] {$T8$};
\node[state] (T8) [below left=of T6] {$T8$};
\node[state] (T9) [below left=of T4] {$T9$};
\node[state] (T9) [below left=of T2] {$T9$};
\node[state] (T9) [below left=of T5] {$T9$};
\node[state] (T10) [below left=of T8] {$T10$};
\node[state] (T10) [below left=of T9] {$T10$};
\node[state] (T10) [below left=of T7] {$T10$};
%\tikzset{mystyle/.style={-,double=orange}}
%\tikzset{every node/.style={fill=white}}
%\path (T3) edge [mystyle] node {$3$} (T1)
% (D) edge [mystyle] node {$10$} (B)
% (L) edge [mystyle] node {$10$} (M)
% (T1) edge [mystyle] node {$10$} (T2);
\tikzset{mystyle/.style={double=orange}}
\path (T1) edge [mystyle] node {$18$} (T2);
(T1) edge [mystyle] node {$12$} (T3);
(T1) edge [mystyle] node {$9$} (T4);
(T1) edge [mystyle] node {$11$} (T5);
(T1) edge [mystyle] node {$14$} (T6);
(T2) edge [mystyle] node {$19$} (T8);
(T2) edge [mystyle] node {$16$} (T9);
(T3) edge [mystyle] node {$23$} (T7);
(T4) edge [mystyle] node {$27$} (T4);
(T4) edge [mystyle] node {$23$} (T9);
(T5) edge [mystyle] node {$13$} (T9);
(T6) edge [mystyle] node {$15$} (T8);
(T7) edge [mystyle] node {$17$} (T10);
(T8) edge [mystyle] node {$11$} (T10);
(T9) edge [mystyle] node {$13$} (T10);
\tikzset{mystyle/.style={relative=false,in=0,out=60,double=orange}}
%\path (L) edge [mystyle] node {$10$} (D);
\end{tikzpicture}
\caption{Directed Acyclic Graph}
\end{figure}
\end{document}
The output should look like this:



