\documentclass{article}
\usepackage{tikz}
\usepackage{amsmath,amssymb}
\usepackage{ifthen}
\usetikzlibrary{arrows,positioning,decorations.pathreplacing,shapes}
\usetikzlibrary{snakes}


\begin{document}

\parindent=0em

\begin{center}
\begin{tikzpicture}

\def\n{7} %nombre de sommets du graphe

%%%%% Dessin des sommets %%%%%
\pgfmathtruncatemacro{\nmoinsun}{\n-1}



\foreach \x in {0,...,\nmoinsun}
\node[circle, very thick, draw=black, fill=red!25] (\x) at (270 + \x * 360/\n:3) {$\x$};


%%% Dessin des flèches noires %%%

\foreach \y in {0,...,\nmoinsun}
\pgfmathtruncatemacro{\z}{mod(\y +1, \n)}
\draw[-triangle 45] (\y) to (\z);


%%%% Dessin des flèches bleues %%%%


\foreach \u in {1,...,\nmoinsun}
\pgfmathtruncatemacro{\v}{mod(\u * 10,\n)}
\pgfmathtruncatemacro{\vplusun}{\v+1}
\pgfmathtruncatemacro{\uplusun}{\u+1}
\ifthenelse{\uplusun=\v}
					 {\draw[-latex, blue, thick, dotted] (\u) to[bend right=45] (\v);}
           {\ifthenelse{\vplusun=\u}
           				{\draw[-latex, blue, thick, dotted] (\u) to[bend left=45] (\v);}
           				{\draw[-latex, blue, thick, dotted] (\u) edge (\v);};};




\draw[-triangle 45] (4,1) -- node[above]{$+1 \mod [\n]$} (6.5,1) ;
\draw[-latex,  blue, thick, dotted] (4,0) -- node[above]{$\times 10 \mod [\n]$} (6.5,0) ;

\end{tikzpicture}
\end{center}

\end{document}