\begin{frame}
    \begin{figure}
        \begin{tikzpicture}[->,scale=1.8, auto,swap]
            % Draw the vertices. First you define a list.
            \foreach \pos/\name in {{(1,0)/a}, {(4,0)/b}, {(5,1)/c},
                                    {(3,1)/d}, {(4,2)/e}, {(5,2)/f},
                                    {(1,2)/g}, {(0,3)/h}, {(2,4)/i},
                                    {(4,3)/j}, {(4,4)/k}, {(5,4)/l}}
                \node[vertex] (\name) at \pos {$\name$};

            % Connect vertices with edges and draw weights
            \foreach \source/ \dest /\pos in {g/a/, b/c/bend right,
                c/b/bend right, d/e/bend right, e/d/, h/g/, g/i/,g/i/bend left, g/i/bend right,
                h/i/, h/i/bend left, g/j/bend right, j/g/,
                j/k/bend right, k/j/bend right, j/f/, f/l/,e/j/,
                l/l/loop right, j/d/}
                \path (\source) edge [\pos] node {} (\dest);
        \end{tikzpicture}
    \end{figure}
\end{frame}

\pgfdeclarelayer{background}
\pgfsetlayers{background,main}

\begin{frame}
    \begin{figure}
        \begin{tikzpicture}[->,scale=1.8, auto,swap]
            % Draw the vertices. First you define a list.
            \foreach \pos/\name in {{(1,0)/a}, {(4,0)/b}, {(5,1)/c},
                                    {(3,1)/d}, {(4,2)/e}, {(5,2)/f},
                                    {(1,2)/g}, {(0,3)/h}, {(2,4)/i},
                                    {(4,3)/j}, {(4,4)/k}, {(5,4)/l}}
                \node[vertex] (\name) at \pos {$15$};

            % Connect vertices with edges and draw weights
            \foreach \source/ \dest /\pos in {g/a/, b/c/bend right,
                c/b/bend right, d/e/bend right, e/d/, h/g/, g/i/,g/i/bend left, g/i/bend right,
                h/i/, h/i/bend left, g/j/bend right, j/g/,
                j/k/bend right, k/j/bend right, j/f/, f/l/,e/j/,
                l/l/loop right, j/d/}
                \path (\source) edge [\pos] node {} (\dest);

             \node<3->[vertex] (a) at (1,0) {$17$};
             \node<5->[vertex] (g) at (1,2) {$21$};
             \node<9->[vertex] (i) at (2,4) {$19$};

            \begin{pgfonlayer}{background}
                \path<2->[selected edge] (g.center) edge [] node {2} (a.center);
                \path<4->[selected edge] (j.center) edge [] node {6} (g.center);
                \path<6->[selected edge] (g.center) edge [bend left] node {1} (i.center);
                \path<7->[selected edge] (g.center) edge [] node {0} (i.center);
                \path<8->[selected edge] (g.center) edge [bend right] node {3} (i.center);
            \end{pgfonlayer}


        \end{tikzpicture}
    \end{figure}
\end{frame}