\documentclass{beamer}
\usepackage{tikz}
\usepackage{verbatim}
\usetikzlibrary{arrows,shapes}

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

\tikzset{
    vertex/.style={
        circle,
        fill=black!25,
        minimum size=20pt,
        inner sep=0pt,
        text height=1ex,
        text depth=1ex,
        label={[weight label]center:\weight},
        label={[pred label]center:\pred}
    },
    pred label/.style={
        font=\tiny,
        xshift=0.3em,
        yshift=-0.8ex,
        text height=1ex,
        text depth=0pt
    },
    weight label/.style={
        font=\tiny,
        xshift=-0.3em,
        yshift=-0.8ex,
        text height=1ex,
        text depth=0pt
    }
}

\tikzstyle{vertexOnly}=[circle,fill=black!25,minimum size=20pt,inner sep=0pt]
\tikzstyle{selected vertex} = [vertex, fill=red!24]
\tikzstyle{edge} = [->,draw,thick]
\tikzstyle{weight} = [font=\small]
\tikzstyle{selected edge} = [draw,line width=5pt,-,red!50]
\tikzstyle{ignored edge} = [draw,line width=5pt,-,black!20]

\begin{frame}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Given Graph                                                       %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{figure}
\begin{tikzpicture}[scale=2.5, auto,swap]
    % First we draw the vertices
    \foreach \pos/\name in {{(0,2)/a}, {(1,2)/b}, {(2,2)/c},
                            {(0,1)/d}, {(1,1)/e}, {(2,1)/f}, 
                            {(0,0)/g}, {(1,0)/h}, {(2,0)/i}}
        \node[vertexOnly] (\name) at \pos {$\name$};
    % Connect vertices with edges and draw weights
    \foreach \source/ \dest /\weight/\style in {a/b/0/, b/c/1/, a/d/2/, e/d/5/,
                                        b/e/3/bend right, e/b/-1/bend right, b/f/4/above, f/i/3/,
                                        i/e/1/, g/h/1/}
        \path (\source) edge[->,\style, thick] node {$\weight$} (\dest);
\end{tikzpicture}
\end{figure}
\end{frame}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Initialisation                                                    %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
    \begin{figure}
        \begin{tikzpicture}[scale=2.5, auto,swap]
            % First we draw the vertices
            \foreach \pos/\name/\weight/\pred in {
                {(0,2)/a/$0$/-},{(1,2)/b/$\infty$/-}, {(2,2)/c/$\infty$/-},
                {(0,1)/d/$\infty$/-}, {(1,1)/e/$\infty$/-}, {(2,1)/f/$\infty$/-}, 
                {(0,0)/g/$\infty$/-}, {(1,0)/h/$\infty$/-}, {(2,0)/i/$\infty$/-}}
                    \node[vertex] (\name) at \pos {$\name$};

            % Connect vertices with edges and draw weights
            \foreach \source/ \dest /\weight/\style in {
                a/b/0/, b/c/1/, a/d/2/, e/d/5/, b/e/3/bend right, 
                e/b/-1/bend right, b/f/4/above, f/i/3/, i/e/1/, 
                g/h/1/}
                    \path (\source) edge[->,\style, thick] node {$\weight$} (\dest);
        \end{tikzpicture}
    \end{figure}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% first iteraton                                                    %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
    \begin{figure}
        \begin{tikzpicture}[scale=2.5, auto,swap]
            % First we draw the vertices
            \foreach \pos/\name/\weight/\pred in {
                {(1,2)/b/$\infty$/-}, {(2,2)/c/$\infty$/-},
                {(0,1)/d/$\infty$/-}, {(1,1)/e/$\infty$/-}, {(2,1)/f/$\infty$/-}, 
                {(0,0)/g/$\infty$/-}, {(1,0)/h/$\infty$/-}, {(2,0)/i/$\infty$/-}}
                    \node[vertex] (\name) at \pos {$\name$};

            % Connect vertices with edges and draw weights
            \foreach \source/ \dest /\weight/\style in {
                a/b/0/, b/c/1/, a/d/2/, e/d/5/, b/e/3/bend right, 
                e/b/-1/bend right, b/f/4/above, f/i/3/, i/e/1/, 
                g/h/1/}
                    \path (\source) edge[->,\style, thick] node {$\weight$} (\dest);
        \end{tikzpicture}
    \end{figure}
\end{frame}

\end{document}