Tikz graphdrawing node distance

Question

I would like to create certain graphs in Tikz with a given node distance. I tried:

\documentclass{amsart}

\usepackage{tikz}
\usetikzlibrary{graphs,graphdrawing,positioning,graphdrawing.layered}

\begin{document}

Setting the distance does not work:
\[
    \begin{tikzpicture}[node distance=10pt]
        \graph[nodes={draw,circle,minimum size=5pt,inner sep=0pt,as=}]
        { 1--[draw=gray]2--[draw=gray]3; 1--[bend left]3; };
    \end{tikzpicture}
\]

Setting the distance works:
\[
    \begin{tikzpicture}
        \graph[layered layout,grow=right,level distance=10pt,nodes={draw,circle,minimum size=5pt,inner sep=0pt,as=}]
        { 1--[draw=gray]2--[draw=gray]3;  };
    \end{tikzpicture}
\]

Adding third edge changes layout:
\[
    \begin{tikzpicture}
        \graph[layered layout,grow=right,level distance=10pt,nodes={draw,circle,minimum size=5pt,inner sep=0pt,as=}]
        { 1--[draw=gray]2--[draw=gray]3;  1--[bend left]3; };
    \end{tikzpicture}
\]

\end{document}

resulting in

Basically I want the first graph but with the node distance of the second graph. So my question is, how can I set the node distance in \graph without specifying a layout (like the layered layout)?

Answer 1

\documentclass{amsart}

\usepackage{tikz}
\usetikzlibrary{graphs,positioning,}

\begin{document}

Setting the distance does not work:
\[
    \begin{tikzpicture}
        \graph[nodes={draw,circle,minimum size=5pt,inner sep=0pt,as=}]
        { 1--[draw=gray]2--[draw=gray]3; 1--[bend left]3; };
    \end{tikzpicture}
\]

Setting the distance works:
\[
    \begin{tikzpicture}
        \graph[nodes={draw,circle,minimum size=5pt,inner sep=0pt,as=}]
        { 1--[draw=gray]2--[draw=gray]3;  };
    \end{tikzpicture}
\]

Adding third edge changes layout:
\[
    \begin{tikzpicture}
        \graph[nodes={draw,circle,minimum size=5pt,inner sep=0pt,as=}]
        { 1--[draw=gray]2--[draw=gray]3;  1--[bend left]3; };
    \end{tikzpicture}
\]

\end{document}