tikz for DAG: give outline and background to labels that are out of the node?

Question

I am using the TikZ and tkz-berge packages to create a direct acyclic graph. I've pasted my code below. I would like the variable labels "variable1", "variable2", etc to have an outline around them and a white background so they are easy to read over the arrows. Is there a way to do this? ( I would like to keep LabelOut=true)

\documentclass[]{article}
\usepackage{tikz}
\usepackage{tikz,fullpage}
\usetikzlibrary{arrows,%
                petri,%
                topaths}%
\usepackage{tkz-berge}
\usepackage[position=top]{subfig}
\usepackage{verbatim}
\begin{document}
\begin{figure}
\centering
\subfloat[]{
\begin{tikzpicture}[scale=0.75,transform shape]
  \Vertex[x=2.221,y=2.379, LabelOut=true, Lpos=-90]{variable1}
  \Vertex[x=-1.786,y=-2.495, LabelOut=true, Lpos=-90]{variable2}
  \Vertex[x=-0.808,y=-0.482, LabelOut=true, Lpos=-90]{variable3}
  \Vertex[x=1.834,y=-5.724, LabelOut=true, Lpos=-90]{variable4}
  \Vertex[x=1.855,y=-1.202, LabelOut=true, Lpos=-90]{variable5}
  \Vertex[x=2.820,y=5.684, LabelOut=true, Lpos=-90]{variable6}
  \Vertex[x=-3.821,y=-0.308, LabelOut=true, Lpos=-90]{variable7}
  \Vertex[x=-1.800,y=-5.955, LabelOut=true, Lpos=-90]{variable8}
  \Vertex[x=-4.797,y=-4.289, LabelOut=true, Lpos=-90]{variable9}
  \Vertex[x=5.243,y=3.474, LabelOut=true, Lpos=-90]{variable10}
  \Vertex[x=4.377,y=-0.046, LabelOut=true, Lpos=-90]{variable11}
  \Vertex[x=1.025,y=-3.360, LabelOut=true, Lpos=-90]{variable12}
  \Vertex[x=-1.086,y=1.824, LabelOut=true, Lpos=-90]{variable13}
  \Vertex[x=1.200,y=0.993, LabelOut=true, Lpos=-90]{variable14}
\tikzstyle{LabelStyle}=[fill=blue,sloped]
\tikzstyle{EdgeStyle}=[post]
  \Edge[](variable3)(variable2)
  \Edge[](variable4)(variable2)
  \Edge[](variable4)(variable5)
  \Edge[](variable5)(variable2)
  \Edge[](variable5)(variable1)
  \Edge[](variable1)(variable14)
  \Edge[](variable6)(variable1)
  \Edge[](variable7)(variable2)
  \Edge[](variable7)(variable13)
  \Edge[](variable8)(variable2)
  \Edge[](variable9)(variable2)
  \Edge[](variable10)(variable1)
  \Edge[](variable11)(variable1)
  \Edge[](variable11)(variable5)
  \Edge[](variable12)(variable2)
  \Edge[](variable12)(variable5)
  \Edge[](variable13)(variable1)
  \Edge[](variable14)(variable3)

\end{tikzpicture}
}

\end{figure}
\end{document}

Answer 1

As, to be honest, I didn't feel like reading the tkz-berge manual, I threw together this example. The pgfonlayer is for drawing the edges in the background, thus behind the labels:

\documentclass{article}
\usepackage{tikz}

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

\newcommand{\Vertex}[2]% pos, name
{ \node[circle,draw,minimum width=0.5cm,inner sep=0] (#2) at (#1) {};
    \node[rounded corners=3pt,below,draw=black,fill=white,inner sep=1.5pt] at (#2.south) {\footnotesize#2};
}

\newcommand{\Edge}[2]%
{ \begin{pgfonlayer}{background}
        \draw (#1) -- (#2);
    \end{pgfonlayer}
}

\begin{document}

\begin{tikzpicture}
    \Vertex{2.221,2.379}{variable1}
    \Vertex{2.221,2.379}{variable1}
    \Vertex{-1.786,-2.495}{variable2}
    \Vertex{-0.808,-0.482}{variable3}
    \Vertex{1.834,-5.724}{variable4}
    \Vertex{1.855,-1.202}{variable5}
    \Vertex{2.820,5.684}{variable6}
    \Vertex{-3.821,-0.308}{variable7}
    \Vertex{-1.800,-5.955}{variable8}
    \Vertex{-4.797,-4.289}{variable9}
    \Vertex{5.243,3.474}{variable10}
    \Vertex{4.377,-0.046}{variable11}
    \Vertex{1.025,-3.360}{variable12}
    \Vertex{-1.086,1.824}{variable13}
    \Vertex{1.200,0.993}{variable14}
    \Edge{variable3}{variable2}
    \Edge{variable4}{variable2}
    \Edge{variable4}{variable5}
    \Edge{variable5}{variable2}
    \Edge{variable5}{variable1}
    \Edge{variable1}{variable14}
    \Edge{variable6}{variable1}
    \Edge{variable7}{variable2}
    \Edge{variable7}{variable13}
    \Edge{variable8}{variable2}
    \Edge{variable9}{variable2}
    \Edge{variable10}{variable1}
    \Edge{variable11}{variable1}
    \Edge{variable11}{variable5}
    \Edge{variable12}{variable2}
    \Edge{variable12}{variable5}
    \Edge{variable13}{variable1}
    \Edge{variable14}{variable3}
\end{tikzpicture}

\end{document}