Node diagram with encompassing circles

Question

I'm attempting to draw an image similar to this one:

However, I only want to draw three nodes as text ("A", "B", "C") with double headed arrows and the larger overlapping circles....

I've had marginal success with the following:

\begin{tikzpicture}[->,>=stealth',shorten >=1pt,auto,node distance=2.8cm,semithick]
  \tikzstyle{style}=[fill=white,draw=none,text=white]
  \tikzstyle{line} = [draw, -latex']

  \node[state]         (A)              {A};
  \node[state]         (B) [right of=A] {B};
  \node[state]         (C) [right of=B] {C};

  \path [line, <->] (A) -- (B);
  \path [line, <->] (B) -- (C);
\end{tikzpicture}

However I cannot get the overlapping outer circles. They should overlap such that the one around A encompasses B, the one around B encompasses A and C, and the one around C encompasses B.

Answer 1

Perhaps :

\documentclass{article}

\usepackage{tikz}
\usetikzlibrary{arrows,calc,through}

\begin{document}

\begin{tikzpicture}[->,>=stealth',shorten >=1pt,auto,node distance=2.8cm,semithick]
  \tikzset{style/.style={fill=white,draw=none,text=white}}
  \tikzset{line/.style = {draw, -latex'}}

  \node        (A)              {A};
  \node        (B) [right of=A] {B};
  \node        (C) [right of=B] {C};
  \node [draw] at (A) [circle through={($(B)+(1,1)$)}] {};
  \node [draw] at (B) [circle through={($(A)-(1,1)$)}] {};
  \node [draw] at (C) [circle through={($(B)-(1,1)$)}] {};
  \path [line, <->] (A) -- (B);
  \path [line, <->] (B) -- (C);
\end{tikzpicture}  
\end{document}