\documentclass[varwidth=true, border=2pt]{standalone}
\usepackage{tikz}
\usetikzlibrary[topaths]
\begin{document}
\newcount\mycount
\tikzstyle{vertexs}=[draw,fill=black,circle,minimum size=4pt,inner sep=0pt]
\begin{tikzpicture}
\foreach \number in {1,...,8}{
\mycount=\number
\advance\mycount by -1
\multiply\mycount by 45
\advance\mycount by 0
\node[draw,circle,inner sep=0.25cm] (N-\number) at (\the\mycount:5.4cm) {};
}
\foreach \number in {9,...,16}{
\mycount=\number
\advance\mycount by -1
\multiply\mycount by 45
\advance\mycount by 22.5
\node[draw,circle,inner sep=0.25cm] (N-\number) at (\the\mycount:5.4cm) {};
}
\foreach \number in {1,...,15}{
\mycount=\number
\advance\mycount by 1
\foreach \numbera in {\the\mycount,...,16}{
\path (N-\number) edge[->,bend right=3] (N-\numbera) edge[<-,bend
left=3] (N-\numbera);
}
}
\end{tikzpicture}
\end{document}