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Is it possible to use the node distance as a variable while expressing coordinates of new nodes with Calc and Positioning libraries? What I want to have is everything within a single piece of code for tikz picture.

This is what I have now.

documentclass[12pt, a4paper]{article}

usepackage{tikz}

usetikzlibrary{automata, positioning, arrows,calc}



begin{document}

begin{tikzpicture}[>=stealth',shorten >=0.5pt,auto,node distance=2cm,semithick,on grid]



  tikzstyle{every state}=[minimum size=20pt, fill=none,draw=black]

  node[state,label=center:$a$,inner sep=0pt] (a) {};

  node[state,label=center:$b$] (b) at ($(a) + sqrt(1/3)*4*(0:1cm) $) {};

  node[state,label=center:$c$] (c) at ($(a) + sqrt(1/3)*4*(-60:1cm)$) {};



  path[->] (a) edge node {$1$} (b)

            (c) edge node[right] {$1$} (b)

      (b) edge [loop right] node[above] {$0,1$} (b);

   path[shorten <=0.5pt,<->]  (a)  edge node[left]{$0$} (c);



end{tikzpicture}

end{document}

I would like to be able to change the below expression with something like:

$(a) + sqrt(1/3)*2*(1:nodedistance)$

Then if I would be copying the code elsewhere, such as a presentations, I would be able to change all these distances at once. Is that possible? If not, introducing a variable in the first line of the TikZ code, and using it afterwards instead the "nodedistance", would also do.

Sorry if it's a dull question, I'm pretty new to TikZ.

AFAIK you cannot simply read off the value of /tikz/node distance. However, in this great answer by @Jake there is a simple way to amend node distance by a pgf key that you can use.

documentclass[12pt, a4paper]{article}

usepackage{tikz}

usetikzlibrary{automata, positioning, arrows,calc}

tikzset{node distance/.append code={

        pgfkeyssetvalue{/tikz/node distance value}{#1}

    }}

begin{document}

begin{tikzpicture}[>=stealth',shorten >=0.5pt,auto,node

distance=2cm,semithick,on grid,

every state/.style={minimum size=20pt, fill=none,draw=black}]

  node[state,label=center:$a$,inner sep=0pt] (a) {};

  node[state,label=center:$b$] (b) at ($(a) + sqrt(4/3)*(0:pgfkeysvalueof{/tikz/node distance value}) $) {};

  node[state,label=center:$c$] (c) at ($(a) + sqrt(4/3)*(-60:pgfkeysvalueof{/tikz/node distance value})$) {};



  path[->] (a) edge node {$1$} (b)

            (c) edge node[right] {$1$} (b)

      (b) edge [loop right] node[above] {$0,1$} (b);

   path[shorten <=0.5pt,<->]  (a)  edge node[left]{$0$} (c);

end{tikzpicture}

end{document}

You can create a macro defnodedistance{1cm} at the begining of the tikzpicture . Later if needed this macro could be redefined .

documentclass[12pt, a4paper]{article}

usepackage{tikz}

usetikzlibrary{automata, positioning, arrows,calc}



begin{document}

begin{tikzpicture}[>=stealth',shorten >=0.5pt,auto,semithick,on grid]



defnodedistance{1cm} % <------------ 



  tikzstyle{every state}=[minimum size=20pt, fill=none,draw=black]

  node[state,label=center:$a$,inner sep=0pt] (a) {};

  node[state,label=center:$b$] (b) at ($(a) + sqrt(1/3)*4*(0:nodedistance) $) {};

  node[state,label=center:$c$] (c) at ($(a) + sqrt(1/3)*4*(-60:nodedistance)$) {};



  path[->] (a) edge node {$1$} (b)

            (c) edge node[right] {$1$} (b)

      (b) edge [loop right] node[above] {$0,1$} (b);

   path[shorten <=0.5pt,<->]  (a)  edge node[left]{$0$} (c);



end{tikzpicture}



begin{tikzpicture}[>=stealth',shorten >=0.5pt,auto,semithick,on grid]



defnodedistance{2cm} % <----------------



  tikzstyle{every state}=[minimum size=20pt, fill=none,draw=black]

  node[state,label=center:$a$,inner sep=0pt] (a) {};

  node[state,label=center:$b$] (b) at ($(a) + sqrt(1/3)*4*(0:nodedistance) $) {};

  node[state,label=center:$c$] (c) at ($(a) + sqrt(1/3)*4*(-60:nodedistance)$) {};



  path[->] (a) edge node {$1$} (b)

            (c) edge node[right] {$1$} (b)

      (b) edge [loop right] node[above] {$0,1$} (b);

   path[shorten <=0.5pt,<->]  (a)  edge node[left]{$0$} (c);



end{tikzpicture}

end{document}