[Tex/LaTex] Draw a graph in Latex with Tikz

graphsnodestikz-arrowstikz-pgf

I am interested in outputting this graph in latex using tikz:

enter image description here

So far I got this:

enter image description here

and my tikz code is 

\begin{tikzpicture}
    \node[shape=circle,draw=black] (A) at (0,0) {A};
    \node[shape=circle,draw=black] (B) at (0,3) {B};
    \node[shape=circle,draw=black] (C) at (2.5,4) {C};
    \node[shape=circle,draw=black] (D) at (2.5,1) {D};
    \node[shape=circle,draw=black] (E) at (2.5,-3) {E};
    \node[shape=circle,draw=black] (F) at (5,3) {F} ;

    \path [->] (A) edge node[left] {$5$} (B);
    \path [->](B) edge node[left] {$3$} (C);
    \path [->](A) edge node[left] {$4$} (D);
    \path [->](D) edge node[left] {$3$} (C);
    \path [->](A) edge node[right] {$3$} (E);
    \path [->](D) edge node[left] {$3$} (E);
    \path [->](D) edge node[top] {$3$} (F);
    \path [->](C) edge node[top] {$5$} (F);
    \path [->](E) edge node[right] {$8$} (F);   
\end{tikzpicture}

I want to know how to draw the arc between nodes B and E and also thicker arcs with their lengths in center. Any help is appreciated

Best Answer

One suggestion, borrowing from David Robertson's comment. A couple of scopes are added, to set the same style easily for all the nodes within them. The weights are set in the center of the line (so left, above etc. are removed), and filled with white, to cover the underlying line. If you really want that, the arrows.meta library lets you set the arrow tip in a different color than the lines.

enter image description here

\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{arrows.meta}
\begin{document}
\begin{tikzpicture}
\begin{scope}[every node/.style={circle,thick,draw}]
    \node (A) at (0,0) {A};
    \node (B) at (0,3) {B};
    \node (C) at (2.5,4) {C};
    \node (D) at (2.5,1) {D};
    \node (E) at (2.5,-3) {E};
    \node (F) at (5,3) {F} ;
\end{scope}

\begin{scope}[>={Stealth[black]},
              every node/.style={fill=white,circle},
              every edge/.style={draw=red,very thick}]
    \path [->] (A) edge node {$5$} (B);
    \path [->] (B) edge node {$3$} (C);
    \path [->] (A) edge node {$4$} (D);
    \path [->] (D) edge node {$3$} (C);
    \path [->] (A) edge node {$3$} (E);
    \path [->] (D) edge node {$3$} (E);
    \path [->] (D) edge node {$3$} (F);
    \path [->] (C) edge node {$5$} (F);
    \path [->] (E) edge node {$8$} (F); 
    \path [->] (B) edge[bend right=60] node {$1$} (E); 
\end{scope}
\end{tikzpicture}
\end{document}
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