How can I plot a graph in beamer step by step

Question

I want to plot this graph in beamer and I don't know how! I want plot step by step this graph..

Step 1:

Step 2:

Step 3:

Step 4:

I write this follow

\documentclass{beamer}

\usepackage{tikz}

\usepackage{verbatim}
\usetikzlibrary{arrows,shapes}


\begin{document}
% Declare layers
\pgfdeclarelayer{background}
\pgfsetlayers{background,main}

\begin{frame}
\frametitle{Prim's algorithm}

%% Adjacency matrix of graph
%% \  a  b  c  d  e  f  g
%% a  x  7     5
%% b  7  x  8  9  7
%% c     8  x     5
%% d  5  9     x 15  6
%% e     7  5 15  x  8  9
%% f           6  8  x 11
%% g              9  11 x

\tikzstyle{vertex}=[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{figure}
\begin{tikzpicture}[scale=1.8, auto,swap]
    % Draw a 7,11 network
    % First we draw the vertices
    \foreach \pos/\name in {{(0,2)/a}, {(2,1)/b}, {(4,1)/c},
                            {(0,0)/d}, {(3,0)/e}, {(2,-1)/f}, {(4,-1)/g}}
        \node[vertex] (\name) at \pos {$\name$};
    % Connect vertices with edges and draw weights
    \foreach \source/ \dest /\weight in {b/a/7, c/b/8,d/a/5,d/b/9,
                                         e/b/7, e/c/5,e/d/10,
                                         f/d/6,f/e/8,
                                         g/e/9,g/f/11}
        \path[edge] (\source) -- node[weight] {$\weight$} (\dest);
    % Start animating the vertex and edge selection. 
    \foreach \vertex / \fr in {a/1,b/2,d/3,c/3}
        \path<\fr-> node[selected vertex] at (\vertex) {$\vertex$};
    % For convenience we use a background layer to highlight edges
    % This way we don't have to worry about the highlighting covering
    % weight labels. 
    \begin{pgfonlayer}{background}
        \pause
        \foreach \source / \dest in {b/a,d/a,d/b,c/b,e/b}
            \path<+->[selected edge] (\source.center) -- (\dest.center);
       % \foreach \source / \dest / \fr in {d/b/4,d/e/5,e/f/5,b/c/6,f/g/7}
          %  \path<\fr->[ignored edge] (\source.center) -- (\dest.center);
    \end{pgfonlayer}
\end{tikzpicture}
\end{figure}

\end{frame}

\end{document}

and problem is 1- my edges of graph is directed but this graph is not 2- in my graph steps are Sometimes chose double which means that in step b and d both chosen by a but this command step by step!!

Answer 1

To make things only appear not immediately on a frame you can use \onslide<2-> What you want to appear\onslide<1->. Everything you write in between the two \onslide commands will only be visible on the second part of the frame. So in your example you want something like that:

\begin{frame}
    \begin{tikzpicture}
         %Draw your graph(always visible)
         \onslide<2->
         %Draw the red lines(only visible on the second part of the frame)
         \onslide<1->
    \end{tikzpicture}
    \pause
\end{frame}

The last \pause is necessary so that there is a chance to enter the second part of the frame where the red lines are shown.