File:Duals graphs.svg

 \documentclass{article}
 \thispagestyle{empty}
 \usepackage{tikz}
 \usetikzlibrary{calc}
 \begin{document}
 \begin{tikzpicture}[node distance=2.5cm,semithick]
  \tikzstyle{origVertex}      = [draw, blue, fill, shape=circle]
  \tikzstyle{dualVertex}      = [draw, red,  fill, shape=circle]
  \tikzstyle{invisibleVertex} = [shape=circle]
  \tikzstyle{origEdge}        = [blue]
  \tikzstyle{dualEdge}        = [red, densely dashed]
  \node[origVertex]      (0)                      {};
  \node[invisibleVertex] (i1) [right       of=0]  {};
  \node[origVertex]      (1)  [right       of=i1] {};
  \node[origVertex]      (2)  [below right of=1]  {};
  \node[origVertex]      (3)  [below left  of=2]  {};
  \node[invisibleVertex] (i2) [left        of=3]  {};
  \node[origVertex]      (4)  [left        of=i2] {};
  \path (0) edge[origEdge] (1)
            edge[origEdge] (4)
        (1) edge[origEdge] (2)
            edge[origEdge] (3)
            edge[origEdge] (4)
        (2) edge[origEdge] (3)
        (3) edge[origEdge] (4);
  \path let
         \p1 = (0),
         \p2 = (1),
         \p3 = (4)
        in
         node[dualVertex] (d0) at (\x1/3+\x2/3+\x3/3,\y1/3+\y2/3+\y3/3) {};
  \path let
         \p1 = (1),
         \p2 = (3),
         \p3 = (4)
        in
         node[dualVertex] (d1) at (\x1/3+\x2/3+\x3/3,\y1/3+\y2/3+\y3/3) {};
  \path let
         \p1 = (1),
         \p2 = (2),
         \p3 = (3)
        in
         node[dualVertex] (d2) at (\x1/3+\x2/3+\x3/3,\y1/3+\y2/3+\y3/3) {};
  \node[dualVertex]       (d3) [below left of=3] {};
  \path (d0) edge[dualEdge] (d1)
             edge[dualEdge, out= 120, in=-170, looseness=4]   (d3)
             edge[dualEdge, out=-150, in= 170, looseness=2.5] (d3)
        (d1) edge[dualEdge] (d2)
             edge[dualEdge] (d3)
        (d2) edge[dualEdge, out=  35, in=   0, looseness=2]   (d3)
             edge[dualEdge, out= -90, in=  20, looseness=1.5] (d3);
 \end{tikzpicture}
 \end{document}