Problema do Tikzpicture: Especificamente para a família "\Vertex", como posiciono abaixo ou acima do nó

Question

No diagrama, quero mover t=0 abaixo (ou acima) do nó sem ajustar para \drawou \pathcódigo \node. Posso anexar algum pequeno trecho de código, como label=above{...}, anchor=southou algo mais em algum lugar do meu código? Parece que preciso ajustar \Vertex..., mas não sei onde acrescentar algo para alterar o rótulo do nó.

Meu código atual é:

\documentclass[12pt]{article}
\usepackage{tikz}
\usepackage{verbatim}
\usepackage{tkz-berge}
\usetikzlibrary{trees, fit,shapes,arrows}
\usepackage{tkz-graph}
\begin{document}
  %banks path
.\begin{tikzpicture}[scale=3] 

...\GraphInit[vstyle=Classic]   

...\tikzset{EdgeStyle/.style={->,font=\scriptsize}}=[circle,draw]   

......\Vertex[x=0,y=1.5]{t=0}   

......\Vertex[x=1,y=1.5]{t=1}   

......\Vertex[x=2,y=1.5]{t=2}   

......\Edges\[label = $1+r$\]\(t=0,t=1\)

......\Edges\[label = $1+r$\]\(t=1,t=2\)

.\end{tikzpicture}   
\end{document}

Passei mais de 3 horas construindo meu diagrama para ficar exatamente como eu queria, e este é meu problema final.

Answer 1

 \documentclass[a4paper,landscape]{article}
 \usepackage[left=1cm]{geometry}
 \usepackage{amsmath}
 \usepackage{xcolor}
 \usepackage{tkz-berge}
 \usetikzlibrary{fit,shapes,arrows}
 \begin{document}
 %(tri) stock's path
 \centering
 \begin{tikzpicture}[scale=3]
    \GraphInit[vstyle=Classic]
    \SetUpVertex[Lpos=-90]
      \tikzset{VertexStyle/.style = {shape=circle, fill=black,
                           minimum size=13pt,inner sep=0pt}
         }
        \Vertex[x=0,y=1.5]{S$_0$}
        \Vertex[x=1,y=2]{uS$_0$}
        \Vertex[x=1,y=1]{d$S_0$}
        \Vertex[x=2,y=1.5]{ud$S_0$}
        \Vertex[x=2,y=2.5]{u$^2$S$_0$}
        \Vertex[x=2,y=.5]{d$^2S_0$}
        \tikzset{EdgeStyle/.style={->,font=\scriptsize},{below=15pt}}
            \Edge[label = $\widetilde{p}$](S$_0$)(uS$_0$) 
            \Edges[label = $1-\widetilde{p}$](S$_0$,d$S_0$)
            \Edges[label = $\widetilde{p}$](uS$_0$,u$^2$S$_0$)
            \Edges[label = $1-\widetilde{p}$](uS$_0$,ud$S_0$)
            \Edges[label = $1-\widetilde{p}$](d$S_0$,d$^2S_0$)
            \Edges[label = $\widetilde{p}$](d$S_0$,ud$S_0$)
 \end{tikzpicture}    
  \\
 %banks path
 \begin{tikzpicture}[scale=3]
    \GraphInit[vstyle=Classic]
    \SetUpVertex[Lpos=-90]
     \tikzset{VertexStyle/.style = {shape=circle, fill=black,
                           minimum size=13pt,inner sep=0pt}
         }
        \Vertex[x=0,y=1.5,]{t=0}
        \Vertex[x=1,y=1.5]{t=1}
        \Vertex[x=2,y=1.5]{t=2}
           \tikzset{EdgeStyle/.style={->,font=\scriptsize,above,sloped,midway}}
              \Edges[label = $1+r$](t=0,t=1)
              \Edges[label = $1+r$](t=1,t=2)

   \end{tikzpicture}
 \end{document}

Eu modifiquei o código aqui

 \documentclass[a4paper,landscape]{article}
 \usepackage[left=1cm]{geometry}
 \usepackage{amsmath}
 \usepackage{xcolor}
 \usepackage{tkz-berge}
 \usetikzlibrary{fit,shapes,arrows}
 \begin{document}
 %(tri) stock's path
 \centering
 \begin{tikzpicture}[scale=3]
    \GraphInit[vstyle=Classic]
    \SetUpVertex[Lpos=-90]
      \tikzset{VertexStyle/.style = {shape=circle, fill=black,
                           minimum size=13pt,inner sep=0pt}
         }
        \Vertex[x=0,y=1.5]{S$_0$}
        \Vertex[x=1,y=2]{uS$_0$}
        \Vertex[x=1,y=1]{d$S_0$}
        \Vertex[x=2,y=1.5]{ud$S_0$}
        \Vertex[x=2,y=2.5]{u$^2$S$_0$}
        \Vertex[x=2,y=.5]{d$^2S_0$}

        %\tikzset{EdgeStyle/.style={->,font=\scriptsize,below=15pt}}
         \tikzset{EdgeStyle/.style={->,font=\scriptsize,above,sloped,midway}}
            \Edge[label = $\widetilde{p}$](S$_0$)(uS$_0$) 
            \Edges[label = $1-\widetilde{p}$](S$_0$,d$S_0$)
            \Edges[label = $\widetilde{p}$](uS$_0$,u$^2$S$_0$)
            \Edges[label = $1-\widetilde{p}$](uS$_0$,ud$S_0$)
            \Edges[label = $1-\widetilde{p}$](d$S_0$,d$^2S_0$)
            \Edges[label = $\widetilde{p}$](d$S_0$,ud$S_0$)
 \end{tikzpicture}    
  \\
 %banks path
 \begin{tikzpicture}[scale=3]
    \GraphInit[vstyle=Classic]
    \SetUpVertex[Lpos=-90]
     \tikzset{VertexStyle/.style = {shape=circle, fill=black,
                           minimum size=13pt,inner sep=0pt}
         }
        \Vertex[x=0,y=1.5,]{t=0}
        \Vertex[x=1,y=1.5]{t=1}
        \Vertex[x=2,y=1.5]{t=2}
           \tikzset{EdgeStyle/.style={->,font=\scriptsize,above,sloped,midway}}
              \Edges[label = $1+r$](t=0,t=1)
              \Edges[label = $1+r$](t=1,t=2)

   \end{tikzpicture}
 \end{document}