\documentclass{article}
\thispagestyle{empty}
\usepackage{tikz}

\def\nodeDist{2.5cm}
\tikzstyle{origVertex}      = [draw, blue, fill, shape=circle]
\tikzstyle{newVertex}       = [draw, red,  fill, shape=circle]
\tikzstyle{invisibleVertex} = [shape=circle]
\tikzstyle{origEdge}      = [blue]
\tikzstyle{newEdge}       = [red, densely dashed]
\tikzstyle{invisibleEdge} = [draw opacity=0]

\begin{document}
\begin{tikzpicture}[node distance=\nodeDist,semithick]
 \node[origVertex] (0)              {};
 \node[origVertex] (1) [right of=0] {};
 \node[origVertex] (2) [above of=0] {};
 \node[origVertex] (3) [above of=1] {};
 \node[origVertex] (4) [above of=2] {};
 \path (0) edge[origEdge, out=-45, in=-135]               node[invisibleVertex] (m0) {} (1)
           edge[origEdge, out= 45, in= 135]               node[invisibleVertex] (m1) {} (1)
           edge[origEdge]                                 node[invisibleVertex] (m2) {} (2)
       (1) edge[origEdge]                                 node[invisibleVertex] (m3) {} (3)
       (2) edge[origEdge]                                 node[invisibleVertex] (m4) {} (3)
           edge[origEdge]                                 node[invisibleVertex] (m5) {} (4)
       (3) edge[origEdge, out=125, in=  55, looseness=30] node[invisibleVertex] (m6) {} (3);
 \path (m0) edge[invisibleEdge, out= 135, in=-135]                (m1)
            edge[invisibleEdge, out=  45, in= -45]                (m1)
            edge[invisibleEdge, out=-145, in=-135, looseness=1.7] (m2)
            edge[invisibleEdge, out= -35, in= -45, looseness=1.7] (m3)
       (m1) edge[invisibleEdge]                                   (m2)
            edge[invisibleEdge]                                   (m3)
       (m2) edge[invisibleEdge]                                   (m4)
            edge[invisibleEdge, out= 135, in=-135]                (m5)
       (m3) edge[invisibleEdge]                                   (m4)
            edge[invisibleEdge, out=  45, in=  15]                (m6)
       (m4) edge[invisibleEdge]                                   (m5)
            edge[invisibleEdge, out=  90, in= 165]                (m6)
       (m5) edge[invisibleEdge, out= 125, in=  55, looseness=30]  (m5)
       (m6) edge[invisibleEdge, out=-125, in= -55, looseness=15]  (m6);
\end{tikzpicture}
\begin{tikzpicture}[node distance=\nodeDist,semithick]
 \node[origVertex] (0)              {};
 \node[origVertex] (1) [right of=0] {};
 \node[origVertex] (2) [above of=0] {};
 \node[origVertex] (3) [above of=1] {};
 \node[origVertex] (4) [above of=2] {};
 \path (0) edge[origEdge, out=-45, in=-135]               node[newVertex] (m0) {} (1)
           edge[origEdge, out= 45, in= 135]               node[newVertex] (m1) {} (1)
           edge[origEdge]                                 node[newVertex] (m2) {} (2)
       (1) edge[origEdge]                                 node[newVertex] (m3) {} (3)
       (2) edge[origEdge]                                 node[newVertex] (m4) {} (3)
           edge[origEdge]                                 node[newVertex] (m5) {} (4)
       (3) edge[origEdge, out=125, in=  55, looseness=30] node[newVertex] (m6) {} (3);
 \path (m0) edge[newEdge, out= 135, in=-135]                (m1)
            edge[newEdge, out=  45, in= -45]                (m1)
            edge[newEdge, out=-145, in=-135, looseness=1.7] (m2)
            edge[newEdge, out= -35, in= -45, looseness=1.7] (m3)
       (m1) edge[newEdge]                                   (m2)
            edge[newEdge]                                   (m3)
       (m2) edge[newEdge]                                   (m4)
            edge[newEdge, out= 135, in=-135]                (m5)
       (m3) edge[newEdge]                                   (m4)
            edge[newEdge, out=  45, in=  15]                (m6)
       (m4) edge[newEdge]                                   (m5)
            edge[newEdge, out=  90, in= 165]                (m6)
       (m5) edge[newEdge, out= 125, in=  55, looseness=30]  (m5)
       (m6) edge[newEdge, out=-125, in= -55, looseness=15]  (m6);
\end{tikzpicture}
\begin{tikzpicture}[node distance=\nodeDist,semithick]
 \node[invisibleVertex] (0)              {};
 \node[invisibleVertex] (1) [right of=0] {};
 \node[invisibleVertex] (2) [above of=0] {};
 \node[invisibleVertex] (3) [above of=1] {};
 \node[invisibleVertex] (4) [above of=2] {};
 \path (0) edge[invisibleEdge, out=-45, in=-135]               node[newVertex] (m0) {} (1)
           edge[invisibleEdge, out= 45, in= 135]               node[newVertex] (m1) {} (1)
           edge[invisibleEdge]                                 node[newVertex] (m2) {} (2)
       (1) edge[invisibleEdge]                                 node[newVertex] (m3) {} (3)
       (2) edge[invisibleEdge]                                 node[newVertex] (m4) {} (3)
           edge[invisibleEdge]                                 node[newVertex] (m5) {} (4)
       (3) edge[invisibleEdge, out=125, in=  55, looseness=30] node[newVertex] (m6) {} (3);
 \path (m0) edge[newEdge, out= 135, in=-135]                (m1)
            edge[newEdge, out=  45, in= -45]                (m1)
            edge[newEdge, out=-145, in=-135, looseness=1.7] (m2)
            edge[newEdge, out= -35, in= -45, looseness=1.7] (m3)
       (m1) edge[newEdge]                                   (m2)
            edge[newEdge]                                   (m3)
       (m2) edge[newEdge]                                   (m4)
            edge[newEdge, out= 135, in=-135]                (m5)
       (m3) edge[newEdge]                                   (m4)
            edge[newEdge, out=  45, in=  15]                (m6)
       (m4) edge[newEdge]                                   (m5)
            edge[newEdge, out=  90, in= 165]                (m6)
       (m5) edge[newEdge, out= 125, in=  55, looseness=30]  (m5)
       (m6) edge[newEdge, out=-125, in= -55, looseness=15]  (m6);
\end{tikzpicture}
\end{document}