How to make curved arrows on graphs?

Question

I'm trying to make a graph like this, but I have not been able to draw the curved arrow in the center.

Here is what I have:

\begin{figure}
\centering
\begin{tikzpicture}
%% vertices
\draw[fill=black] (0,0) circle (3pt);
\draw[fill=black] (1,0) circle (3pt);
\draw[fill=white] (2,0) circle (3pt);
\draw[fill=black] (3.3,0) circle (3pt);
\draw[fill=black] (4.3,0) circle (3pt);
\draw[fill=white] (5.3,0) circle (3pt);
\draw[fill=white] (6.6,0) circle (3pt);
\draw[fill=white] (7.6,0) circle (3pt);
\draw[fill=black] (8.6,0) circle (3pt);
%% vertex labels
\node at (0, .8) {1};
\node at (0, -.3) {x};
\node at (1, -.3) {y};
\node at (2, -.3) {z};
\node at (3.3, .8) {2};
\node at (3.3, -.3) {x};
\node at (4.3, -.3) {y};
\node at (5.3, -.3) {z};
\node at (6.6, .8) {3};
\node at (6.6, -.3) {x};
\node at (7.6, -.3) {y};
\node at (8.6, -.3) {z};
%%% edges
\draw[thick] (0,0) -- (1,0) -- (1.9,0);
\draw[thick] (3.3,0) -- (4.3,0) -- (5.2,0);
\draw[thick] (6.7,0) -- (7.5,0);
\draw[thick] (7.7,0) -- (8.6,0);
\end{tikzpicture}
\caption{Existe una jugada entre el tablero 1 y el tablero 3.}
\end{figure}

Which looks like this:

Answer 1

You can use an edge:

\draw[red, dotted, thick, shorten >=3pt, shorten <=3pt]  
    (X2) edge[out=45, in=135, -stealth] (Z2);

which yields

Suggestions:

• Use \coordinates to define points with names. In the code below I defined coordinates (X2) and (Z2).
• Place the \nodes using the named coordinates and use a \tikzset to define a style to adjust the position of the \node label relative to the coordinate. I defined the style Node Position to specify the location of the labels.

Code:

\documentclass{article}
\usepackage{tikz}
\begin{document}
\begin{tikzpicture}
\coordinate (X2) at (3.3, 0);
\coordinate (Z2) at (5.3, 0);
\tikzset{Node Position/.style={yshift=-0.3cm}}
%% vertices
\draw[fill=black] (0,0) circle (3pt);
\draw[fill=black] (1,0) circle (3pt);
\draw[fill=white] (2,0) circle (3pt);
\draw[fill=black] (X2) circle (3pt);
\draw[fill=black] (4.3,0) circle (3pt);
\draw[fill=white] (Z2) circle (3pt);
\draw[fill=white] (6.6,0) circle (3pt);
\draw[fill=white] (7.6,0) circle (3pt);
\draw[fill=black] (8.6,0) circle (3pt);
%% vertex labels
\node at (0, .8) {1};
\node at (0, -.3) {x};
\node at (1, -.3) {y};
\node at (2, -.3) {z};
\node at (3.3, .8) {2};
\node [Node Position] at (X2) {x};
\node at (4.3, -.3) {y};
\node [Node Position] at (Z2) {z};
\draw[red, dotted, thick, shorten >=3pt, shorten <=3pt]  (X2) edge[out=45, in=135, -stealth] (Z2);
\node at (6.6, .8) {3};
\node at (6.6, -.3) {x};
\node at (7.6, -.3) {y};
\node at (8.6, -.3) {z};
%%% edges
\draw[thick] (0,0) -- (1,0) -- (1.9,0);
\draw[thick] (3.3,0) -- (4.3,0) -- (5.2,0);
\draw[thick] (6.7,0) -- (7.5,0);
\draw[thick] (7.7,0) -- (8.6,0);
\end{tikzpicture}
\end{document}