Move graph nodes on a circular path while keeping the circle

Question

I would like to show nodes on a graph. The graph shape should be a circle. I would like to move the nodes while keep the circular shape. The following is what I can create with four nodes and it actually looks good:

\tikzstyle{cblue}=[circle, draw, thin,fill=cyan!20, scale=0.5]

\begin{tikzpicture}[->,>=stealth',shorten >=1pt,auto,node distance=3cm,thick,main node/.style={rectangle,fill=blue!20,draw,font=\sffamily\Large\bfseries}]
\draw[help lines] (-1,-1) grid (1,1);
\node[cblue] (1) at ( 90:1 ) {1};
\node[cblue] (2) at ( 0:1 ) {2};
\node[cblue] (3) at ( -90:1) {3};
\node[cblue] (4) at ( 180:1) {4};

\path[every node/.style={font=\sffamily\small}]
(1) edge  [bend left]  node [right] {} (2)
(2) edge  [bend left]  node [right] {} (3)
(3) edge  [bend left]  node [right] {} (4)
(4) edge  [bend left]  node [right] {} (1) ;
\end{tikzpicture}

However, as I move the nodes along the circle, the circular shape is not preserved. Here are some modified coordinates:

\node[cblue] (1) at ( 90:1 ) {1};
\node[cblue] (2) at ( 30:1 ) {2};
\node[cblue] (3) at ( 340:1) {3};
\node[cblue] (4) at ( 180:1) {4};

I guess this is because as explained here, bend right option is not exactly a circular pattern.

I have looked into pgf's "through library" and though I could draw a circle that passes through the nodes, but what I really want is a circle that is broken into four pieces, each piece separated by two nodes.

I appreciate if someone could tell me how I can do this?

Answer 1

If you don't mind parameterizing a bunch of stuff (including the scale) the arcs can be drawn fairly precisely, by calculating the angle on the main circle subtended by the chord formed by the radii of the nodes.

There will still be a slight error in the arcs caused by pgf "backing-up" along the tangent of the endpoint of the arc. In the CVS version of pgf the bending library (not used here) can overcome this.

\documentclass[border=0.125cm]{standalone}

\usepackage{tikz}
\usetikzlibrary{decorations.markings}

\begin{document}

\def\r{1cm}% radius of circle
\def\R{0.25cm}% radius of node
\def\s{2}% scaling factor
\def\o{1pt}% outer sep
\def\shO{0}% shorten angle out
\def\shI{2}% shorten angle in

% chord angle = 2*asin(R/(2*r))
%
% Here the radius R must also include the outer sep
% and the radius r must include the scaling factor
%
\pgfmathparse{2*asin((\R+\o)/(2*\r*\s))+\shO}\let\aO=\pgfmathresult
\pgfmathparse{2*asin((\R+\o)/(2*\r*\s))+\shI}\let\aI=\pgfmathresult

\begin{tikzpicture}[scale=\s, cblue/.style={circle, draw, fill=cyan!20, font=\footnotesize, outer sep=\o, minimum size=\R*2}, >=stealth]

\draw [ultra thick, gray!50] circle [radius=\r];

\node[cblue] (1) at ( 90:\r ) {1};
\node[cblue] (2) at ( 30:\r ) {2};
\node[cblue] (3) at ( 340:\r) {3};
\node[cblue] (4) at ( 180:\r) {4};

% By default there will still be an error
% in the paths due to PGF `backing up'
% to draw the arrow head.
\draw [->] (90-\aO:\r)  arc (90-\aO:30+\aI:\r);
\draw [->] (30-\aO:\r)  arc (30-\aO:-20+\aI:\r);
\draw [->] (340-\aO:\r) arc (340-\aO:180+\aI:\r);
\draw [->] (180-\aO:\r) arc (180-\aO:90+\aI:\r);

\end{tikzpicture}

\end{document}

Answer 2

Using bend left won't be useful here. But use of in and out angles with carefully chosen looseness may help. Adjust them to suit your needs.

\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{arrows}
\tikzset{cblue/.style={circle, draw, thin,fill=cyan!20, scale=0.5}}

\begin{document}
\begin{tikzpicture}[->,>=stealth',shorten >=1pt,auto,node distance=3cm,thick,main node/.style={rectangle,fill=blue!20,draw,font=\sffamily\Large\bfseries}]
\draw[help lines] (-1,-1) grid (1,1);
\draw[gray] (0,0) circle (1cm);
\node[cblue] (1) at ( 90:1 ) {1};
\node[cblue] (2) at ( 30:1 ) {2};
\node[cblue] (3) at ( 340:1) {3};
\node[cblue] (4) at ( 180:1) {4};

\path[every node/.style={font=\sffamily\small}]
(1) edge  [in=125,out=0,looseness=.7]  node [right] {} (2)
(2) edge  [in=80,out=-65,looseness=.85]  node [right] {} (3)
(3) edge  [in=280,out=-115,looseness=1.25]  node [right] {} (4)
(4) edge  [in=185,out=90,looseness=.8]  node [right] {} (1) ;
\end{tikzpicture}
\end{document}

Answer 3

It seems that the focal point is to keep the circle reserved when nodes are moved along the circle. To this end, this attempt proposes arccommands.

\draw (alpha:radius) arc (alpha:beta:radius);  % alpha=start angle, beta=end angle

Code:

\documentclass[border=10pt]{standalone}
\usepackage{tikz}
\usetikzlibrary{arrows}
\tikzset{cblue/.style={circle, draw, thin,fill=cyan!20, scale=0.5}
}

\begin{document}
\begin{tikzpicture}[->,>=stealth',shorten >=5pt,auto,thick, scale=2]
\draw [help lines] (-1,-1) grid (1,1);
\draw (90:1)     arc (90:30:1);
\draw (30:1)     arc (30:-20:1);
\draw (-20:1)    arc (-20:-180:1);
\draw (-180:1)   arc (-180:-270:1);
\node[cblue] (1) at ( 90:1 ) {1};
\node[cblue] (2) at ( 30:1 ) {2};
\node[cblue] (3) at ( 340:1) {3};
\node[cblue] (4) at ( 180:1) {4};
\end{tikzpicture}

\hspace{1cm}

\begin{tikzpicture}[->,>=stealth',shorten >=5pt,auto,thick,scale=2] 
\draw[help lines] (-1,-1) grid (1,1);
\draw (120:1)    arc (120:30:1);
\draw (30:1)     arc (30:-60:1);
\draw (-60:1)    arc (-60:-200:1);
\draw (-200:1)   arc (-200:-240:1);
\node[cblue] (1) at ( 120:1 ){1};
\node[cblue] (2) at ( 30:1 )  {2};
\node[cblue] (3) at ( 300:1) {3};
\node[cblue] (4) at ( 160:1) {4};
\end{tikzpicture}
\end{document}