Move a tikz node somewhat below in relative positioning

Question

I have the following code (stripped down from a much larger one).

(I understand that there are numerous questions (and answers including this excellent one) on relative positioning of nodes, but they do not seem to solve my problem. Before you mark my question as duplicate, please make it sure that it really addresses my issue ie. use relative positioning and not absolute positioning.)

\documentclass{article}

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

\begin{document}

\begin{tikzpicture}[node distance=40.0mm, auto]
  \node[state] (3) {3}; 
  \node[state] (1) [above left=of 3]  {1}; 
  \node[state] (2) [above right=of 3] {2}; 
\end{tikzpicture}

\end{document}

The output looks like this.

I would like to move node 3 somewhat below its current position. I have tried many ways of doing this using relative positioning (and without using absolute positioning), without success. How do I do this?

Answer 1

Just to sum up the above comments and get future readers an overview about the discussed answers:

Prerequisites:

\usetikzlibrary{positioning}

Per node distance definition:

\node (id) [below left=<x-value> and <y-value> of <reference>] {<text>};

Global distance definition:

\begin{tikzpicture}[node distance=<x-value> and <y-value>]
 \node (id) [below left=of <reference>] {<text>};
 % ...

Answer 2

For this kind of diagrams where you are putting many nodes relative to one another, a matrix approach would be more suited. You have to use \usetikzlibrary{matrix} and declare the nodes as the elements of a matrix. The row and column separations, node styles etc can be declared via \tikzset. You can refer to those nodes using the name of the matrix say (m) like (m-1-1) where (m-2-3) 2 is the row and 3 is the column (indices).

Here is a sample code:

\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{matrix,automata}   %% load the library

\begin{document}

\begin{tikzpicture}
  \tikzset{   %%% define the parameters for once
    mstyle/.style={column sep=4cm, row sep=6cm,nodes={state},font=\bfseries},
    line/.style={draw,very thick,blue,-latex},
  }
  \matrix(m)[matrix of nodes,ampersand replacement=\&,mstyle]{
    1 \&  \& 2  \\
      \& 3 \&   \\
    4 \& 5 \& 6  \\
  };
    \draw[line](m-1-1.east)-- (m-1-3.west);
\end{tikzpicture}

\end{document}

With row sep = 2cm in \mstyle, we get

And with our very technique \\[2cm], we get

\matrix(m)[matrix of nodes,ampersand replacement=\&,mstyle]{
    1 \&  \& 2  \\[2cm]
      \& 3 \&   \\
    4 \& 5 \& 6  \\

For more details, please refer to pgfmanual, page no 654 (in my copy of v3) section 57.

However, I accept that I am not aware of how your final diagram will be. Hence, you are the better judge of choices you have.