Tikz: horizontal centering of group of nodes

Question

I need to align each row of the graph to the center. I am trying to do it with xshift. Here the code:

    \begin{tikzpicture}[node distance=1.5cm, auto, text centered]
    \tikzstyle{every node}=[draw,ball];
    \begin{scope}[xshift=1.5cm]
        \node (A) {A};
        \node [right of=A] (B) {B};
        \node [right of=B] (C) {C};
        \node [right of=C] (D) {D};
    \end{scope}
    \begin{scope}[yshift=-1.5cm]
        \node (AB) {AB};
        \node [right of=AB] (AC) {AC};
        \node [right of=AC] (AD) {AD};
        \node [right of=AD] (BC) {BC};
        \node [right of=BC] (BD) {BD};
        \node [right of=BD] (CD) {CD};
    \end{scope}
    \begin{scope}[yshift=-3cm,node distance=2cm,xshift=1cm]
        \node (ABC) {ABC};
        \node [right of=ABC] (ABD) {ABD};
        \node [right of=ABD] (ACD) {ACD};
        \node [right of=ACD] (BCD) {BCD};
    \end{scope}
    \begin{scope}[xshift=4cm, yshift=-4.5cm, node distance=2cm]
        \node (ABCD) {ABCD};
    \end{scope}
\end{tikzpicture}

Is there any other way to do it? Do not like to change xshift values every time.

Solution

You can make each row its own matrix, allowing you to effectively group a set of nodes into one.

Your Example

\begin{tikzpicture}[auto]
    \begin{scope}[]
        \matrix[nodes={draw,ball}, column sep=1cm]{
            \node (A) {A}; &
            \node (B) {B}; &
            \node (C) {C}; &
            \node (D) {D}; \\
            };
    \end{scope}
    \begin{scope}[yshift=-1.5cm]
        \matrix[nodes={draw,ball}, column sep=1cm]{
            \node (AB) {AB}; &
            \node (AC) {AC}; &
            \node (AD) {AD}; &
            \node (BC) {BC}; &
            \node (BD) {BD}; &
            \node (CD) {CD}; \\
        };
     \end{scope}
     \begin{scope}[yshift=-3cm]
        \matrix[nodes={draw,ball}, column sep=1cm]{
            \node (ABC) {ABC}; &
            \node (ABD) {ABD}; &
            \node (ACD) {ACD}; &
            \node (BCD) {BCD}; \\
        };
    \end{scope}
    \begin{scope}[yshift=-4.5cm]
        \matrix[nodes={draw,ball}, column sep=1cm]{
            \node (ABCD) {ABCD}; \\
        };
    \end{scope}
\end{tikzpicture}

Note: be sure to \usetikzlibrary{matrix}

Results in

(I made up my own ball style.)

Comments

[Geoff]

Oh. I just realized you posted a comment referring to matrix. I hope this is useful anyway.

[mindhex]

I thought about making one big matrix, not one matrix per scope, thanks!