How to manually define the center of a node in Tikz?

Question

I would like to ask the following question.

How can I define the center of a node in Tikz?

In the following example, I would like to define the respective bullets to be the respective centers (such that it aligns graphically). Is there an easy way to do that? I would like to avoid defining $3$ or $4$ instead of one.

At the moment, they are not aligned and it looks like this:

%& /home/bernhard/.config/TikzEdtWForms/TikzEdtWForms/0.2.1.0/temp_header
\begin{document}
\usetikzlibrary{patterns,shapes,decorations.pathmorphing,decorations.pathreplacing,calc,arrows}
\usetikzlibrary{arrows}
\begin{tikzpicture}
\node (v2) at (-2,20) {$uvw=\bullet^{2}=xyz$};
\node (v6) at (2,20) {$\bullet^{6}$};
\node (v7) at (0,24) {$abc=\bullet^7=defgh$};
\draw [-open triangle 45] (v2) edge node[above] {}  (v7);
\draw [-open triangle 45] (v7) edge node[above] {}  (v6);
\draw [-open triangle 45] (v2) edge node[above] {}  (v6);
\end{tikzpicture}
\end{document}

This yields the following picture.

I would like to make the bullets of the respective vertices $2$, $6$ and $7$ being the centers of the / aligned with the red crosses (which are not part of the code, but drawn nevertheless).

Thank you very much for the help.

Answer 1

It isn't that difficult to put the nodes on the desired spots, one only has to measure what comes before and after the bullet, and introduce the corresponding xshift. The bigger challenge is to draw the arrows in such a way that they point towards the bullets but stop at the node boundaries. This is a brute-force solution using intersections. (In a perfect world one could generalize the asymmetrical rectangle from the cd library in such a way that it also allows for horizontal shifts of the center. However, the shape defined there stores the shifts of the center in pgf keys, which apply to all of the shapes in a given scope. To use it here, one would have to allow for individual shifts of single nodes, and then do proper book keeping.) The intersections are computed in a pic to make things somewhat more user-friendly. The nodes are created via the center bullet style, which takes two arguments, the stuff before and after the bullet in the center.

\documentclass[tikz,border=3mm]{standalone}
\usetikzlibrary{arrows,intersections,shapes.misc}
\makeatletter
\tikzset{autosave background path/.code={
\ifcsname tikz@fig@name\endcsname
\tikzset{name path=bp\tikz@fig@name}%
\fi}}   
\makeatother    
\begin{document}
\begin{tikzpicture}[center bullet/.code 2 args={%
    \pgfmathsetmacro{\mydw}{0.5*(width("${}\vphantom{\bullet}#2$")-width("$#1{}$"))}%
    \tikzset{xshift=\mydw pt,yshift=0.5ex,text depth=0.25ex,text height=1em,
        autosave background path,
        execute at begin node={$#1\bullet#2$}}},
    pics/connect/.style n args={4}{code={%
     \path[name path=tmp] (#2) -- (#4);
     \tikzset{name intersections={of=tmp and bp#1,by=tmp1},
        name intersections={of=tmp and bp#3,by=tmp2}}
     \draw[pic actions] (tmp1) -- (tmp2);   
    }}]
 \path (-2,20) coordinate (v2) (2,20) coordinate (v6) (0,24) coordinate (v7);
 \node[center bullet={uvw=}{^{2}=xyz}] (n2) at (v2) {};%{$uvw=\bullet^{2}=xyz$};
 \node[center bullet={}{^{6}}] (n6) at (v6){};% {$\bullet^{6}$};
 \node[center bullet={abc=}{^7=defgh}] (n7) at (v7){};% {$abc=\bullet^7=defgh$};
 \path[-open triangle 45] pic{connect={n2}{v2}{n7}{v7}}
    pic{connect={n2}{v2}{n6}{v6}} pic{connect={n7}{v7}{n6}{v6}};
 % just for illustration that the bulltets sit at the right points  
 \path foreach \x in {2,6,7} {(v\x) node[red,draw,cross out]{}};        
\end{tikzpicture}
\end{document}

The red crosses are only to confirm that it works. One can remove them, as well as the shapes.misc library.

Answer 2

\documentclass{article}
\usepackage{amsmath}
\usepackage{tikz}
\usetikzlibrary{arrows}
\begin{document}
\begin{tikzpicture}
  \node[circle,inner sep=0pt] (v2) at (-2,20) {\makebox[0pt][r]{$uvw={}$}$\bullet$\makebox[0pt][l]{$^{2}=xyz$}};
  \node[circle,inner sep=0pt] (v6) at (2,20) {$\bullet$\makebox[0pt][l]{$^{6}$}};
  \node[circle,inner sep=0pt] (v7) at (0,24) {\makebox[0pt][r]{$abc={}$}$\bullet$\makebox[0pt][l]{$^7=defgh$}};
  \draw [-open triangle 45] (v2) edge node[above] {}  (v7);
  \draw [-open triangle 45] (v7) edge node[above] {}  (v6);
  \draw [-open triangle 45] (v2) edge node[above] {}  (v6);
\end{tikzpicture}
\end{document}

Answer 3

Since you propose to manually position the center of the node, I propose the following solution: The node with the text is positioned by trial and error with respect to the node where the arrows point.

There might be a solution with tikzmark but I didn't get there quickly.

PS: your code is not compilable!

\documentclass[border=10pt,tikz]{article}
\usepackage{tikz}
\usetikzlibrary{tikzmark}

\usetikzlibrary{patterns,shapes,decorations.pathmorphing,decorations.pathreplacing,calc,arrows}
\usetikzlibrary{arrows,positioning}
\begin{document}

\begin{tikzpicture}


\node[circle,draw,inner sep=0](v2) at (-2,20){};
\node[circle,draw,inner sep=0](v6) at (2,20){};
\node[circle,draw,inner sep=0](v7) at (0,24){};
\draw [-open triangle 45] (v2) edge node[above] {}  (v7);
\draw [-open triangle 45] (v7) edge node[above] {}  (v6);
\draw [-open triangle 45] (v2) edge node[above] {}  (v6);

\node (v2) at ($(v2.center)+(0.5mm,0)$) {$uvw=\bullet^{2}=xyz$};
\node (v6) at ($(v6.center)+(1mm,0)$)  {$\bullet^{6}$};
\node (v7) at ($(v7.center)+(3.2mm,0)$)  {$abc=\bullet^7=defgh$};

\end{tikzpicture}


\end{document}

Answer 4

Yet another version, using labels. Unfortunately it still requires some manual nudging.

\documentclass{amsart}

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

\begin{document}

\begin{tikzpicture}
\node[label={[shift={(.25,-.02)}]left:$uvw={}$},label={[shift={(-.25,0)}]right:$^2=xyz$}] 
  (v2) at (-2,20) {$\bullet$};
\node[label={[shift={(-.25,0)}]right:$^6$}]
  (v6) at (2,20) {$\bullet$};
\node[label={[shift={(.25,.01)}]left:$abc={}$},label={[shift={(-.25,0)}]right:$^7=defgh$}]
  (v7) at (0,24) {$\bullet$};
\draw [-open triangle 45] (v2) -- (v7);
\draw [-open triangle 45] (v7) -- (v6);
\draw [-open triangle 45] ($(v2)+(4em,0)$) -- (v6);
\end{tikzpicture}

\end{document}