Beamer with Tikz graphs

Question

Following this question of mine, I now need to make a presentation using Beamer.

If you look at the plot below, it has some values on the arrows namely p1, 1-p1, ... I want to put the graph structure first and then when pressing the arrow key get the values showing one by one.
Just writing \pause in front of the nodes doesn't work, that would have been too simple. I don't know how to make it happen, anyone help?

\documentclass{beamer}

\usepackage{tikz}
\usepackage{amssymb}
\usetikzlibrary{arrows,positioning}
\usepackage[english]{babel}
\usepackage{amsmath}

\begin{document}
\begin{frame}
\begin{tikzpicture}[->,>=stealth',shorten >=1pt,auto,node distance=2.5cm,
                thick,main node/.style={rectangle,draw,font=\sffamily\Large    \bfseries}]  

\node[main node] (1) {1};
\node[main node] (2) [below = of 1] {2};
\node[main node] (3) [below = of 2] {3};
\node[main node,draw = none] (4) [right = 2in of 1] {$\varnothing$};
\node[main node,draw = none] (5) [right = 2in of 2] {$\varnothing$};
\node[main node,draw = none] (6) [right = 2in of 3] {$\varnothing$};

\path[every node/.style={font=\sffamily\small}]
(1) edge node [left] {$p_1$} (2)
    edge node [above] {$1-p_1$} (4)
(2) edge node [left] {$p_2$} (3)
    edge node [above] {$1-p_2$} (5)
(3)   edge node [above] {$1-p_3$} (6);
\path[draw,every node/.style={font=\sffamily\small}]
(3.west) -- ([xshift=-2cm]3.west) -- ([xshift=-2cm]1.west) node [midway,left] {$p_3$} -- (1.west); 
\end{tikzpicture}
\end{frame}
\end{document}

Answer 1

You can use visible on style (see Mindmap tikzpicture in beamer (reveal step by step)). This one is used in code below but there are some other options not far away provided by Matthew Leingang, Claudio Fiandrino, Qrrbrbirlbel or Gonzalo Medina just to mention some of them.

\documentclass{beamer}

\usepackage{tikz}
\usepackage{amssymb}
\usetikzlibrary{arrows,positioning}
\usepackage[english]{babel}
\usepackage{amsmath}

\tikzset{
    invisible/.style={opacity=0,text opacity=0},
    visible on/.style={alt=#1{}{invisible}},
    alt/.code args={<#1>#2#3}{%
      \alt<#1>{\pgfkeysalso{#2}}{\pgfkeysalso{#3}} % \pgfkeysalso doesn't change the path
    },
}

\begin{document}
\begin{frame}
\begin{tikzpicture}[->,>=stealth',shorten >=1pt,auto,node distance=2.5cm,
                thick,main node/.style={rectangle,draw,font=\sffamily\Large    \bfseries}]  

\node[main node] (1) {1};
\node[main node] (2) [below = of 1] {2};
\node[main node] (3) [below = of 2] {3};
\node[main node,draw = none] (4) [right = 2in of 1] {$\varnothing$};
\node[main node,draw = none] (5) [right = 2in of 2] {$\varnothing$};
\node[main node,draw = none] (6) [right = 2in of 3] {$\varnothing$};

\path[every node/.style={font=\sffamily\small}]
(1) edge node [left, visible on=<2->] {$p_1$} (2)
    edge node [above, visible on=<2->] {$1-p_1$} (4)
(2) edge node [left, visible on=<3->] {$p_2$} (3)
    edge node [above, visible on=<3->] {$1-p_2$} (5)
(3)   edge node [above, visible on=<4->] {$1-p_3$} (6);
\path[draw,every node/.style={font=\sffamily\small}]
(3.west) -- ([xshift=-2cm]3.west) -- ([xshift=-2cm]1.west) node [midway,left, visible on=<4->] {$p_3$} -- (1.west); 
\end{tikzpicture}
\end{frame}
\end{document}