Sorry it's not a good example of code with tkz-berge but there are a lot of possibilities with tkz-graph and tkz-berge that I made the most simple without great ideas.
You need to find better names. To see the names of vertices you can change Art with Classic
\GraphInit[vstyle=Classic]
\documentclass[]{article}
\usepackage[usenames,dvipsnames]{xcolor}
\usepackage{tkz-berge}
\begin{document}
\begin{tikzpicture}
\GraphInit[vstyle=Art]
\SetGraphUnit{2}
\Vertex{A}
\grCycle[prefix=a,rotation=30,RA=6]{6}
{\SetUpEdge[style={ultra thick},color=red]
\grCycle[prefix=b,RA=3.464]{6} }
\SetVertexArt[MinSize = 4pt]
\grCycle[prefix=c,rotation=30,RA=2]{6}
\grCycle[prefix=d,rotation=30,RA=4]{6}
\NO(d2){e2} \NO(b2){e3}
\NO(b1){e4} \NO(d0){e5}
\SO(d3){e6} \SO(b4){e7}
\SO(b5){e8} \SO(d5){e9}
\NO(a3){f1} \NO(f1){f2}
\NO(a5){f3} \NO(f3){f4}
\Edges(a2,d2,c2,A,c5,d5,a5)
\Edges(a3,d3,c3,A,c0,d0,a0)
\Edges(a4,d4,c4,A,c1,d1,a1)
\Edges(f2,d2,e2,b2,c1,b1,e4,d1)
\Edges(d1,e3,b2,c2,b3,f1)
\Edges(d0,f4,b0,c5,b5,e8,d4,e7,b4,c3,b3,f2)
\Edges(d0,e5,b1,c0,b0,f3,d5,e9,b5,c4,b4,e6,d3,f1)
\SetUpEdge[style={->,ultra thick,double},color=blue]
\Edges(A,b0) \Edges(A,b1)
\end{tikzpicture}
\end{document}
I forgot the rotation :
\begin{tikzpicture}[rotate=30] ....

A better idea to begin this code is :
\begin{tikzpicture}
\GraphInit[vstyle=Art]
\SetVertexArt[MinSize = 4pt]
\SetGraphUnit{2}
\grCycle[prefix=V,RA=4]{6}
\foreach \n in {0,...,5}{%
\begin{scope}[shift=(V\n)]
\grCycle[prefix=V\n,RA=2]{6}
\end{scope}}
\end{tikzpicture}

version 3
\begin{tikzpicture}
\foreach \n in {0,...,3}
{\begin{scope}[shift={({\n*sqrt(3)},\n)},rotate=90]
\pgfmathsetmacro\order{7-\n}
\grEmptyPath[prefix=\n,RA=2]{\order}
\end{scope} }
\foreach \n in {-1,...,-3}
{ \begin{scope}[shift={({\n*sqrt(3)},-\n)},rotate=90]
\pgfmathsetmacro\order{7+\n}
\grEmptyPath[prefix=\n,RA=2]{\order}
\end{scope} }
\end{tikzpicture}
