\begin{tikzpicture}[x=1cm,y=1cm,font=\small,>=Latex,
 original/.style={circle,fill=black,inner sep=0pt,minimum size=4pt},
 internal/.style={circle,draw=black!55,fill=white,inner sep=0pt,minimum size=3pt}]
\node[anchor=west] at (0,4.65) {(a) \(S_3(K_5)\)};
\node[anchor=west] at (5.0,4.65) {(b) Distances to two middle edges};
\foreach \i/\ang in {0/90,1/18,2/-54,3/-126,4/162}
 {\coordinate (v\i) at ({2.1+1.75*cos(\ang)},{2.55+1.75*sin(\ang)});}
\foreach \i/\j in {0/1,0/2,0/3,0/4,1/2,1/3,1/4,2/3,2/4,3/4}{
 \draw[black!40] (v\i)--(v\j);
 \node[internal] at ($(v\i)!1/3!(v\j)$) {};
 \node[internal] at ($(v\i)!2/3!(v\j)$) {};
}
\draw[blue!70!black,line width=1.8pt] ($(v0)!1/3!(v1)$)--($(v0)!2/3!(v1)$);
\draw[orange!85!black,line width=1.8pt] ($(v0)!1/3!(v2)$)--($(v0)!2/3!(v2)$);
\node[above right=2pt] at ($(v0)!.5!(v1)$) {$e$};
\node[left=3pt] at ($(v0)!.5!(v2)$) {$f$};
\foreach \i/\ang in {0/90,1/18,2/-54,3/-126,4/162}{
 \node[original] at (v\i) {};
 \node at ({2.1+2.02*cos(\ang)},{2.55+2.02*sin(\ang)}) {$\i$};
}
\node at (2.1,.32) {25 vertices, 30 edges};
\foreach \y/\j/\edge/\col in {3.7/1/e/blue!70!black,2.55/2/f/orange!85!black}{
 \coordinate (a) at (5.25,\y); \coordinate (b) at (7.35,\y);
 \coordinate (c) at (9.45,\y); \coordinate (d) at (11.55,\y);
 \draw (a)--(d);
 \draw[\col,line width=1.8pt] (b)--(c);
 \node[original,label=below:$0$] at (a) {};
 \node[internal] at (b) {}; \node[internal] at (c) {};
 \node[original,label=below:$\j$] at (d) {};
 \node[below=3pt] at (8.4,\y) {$\edge$};
 \node[above=3pt] at (6.3,\y) {1 step};
 \node[above=3pt] at (10.5,\y) {1 step};
}
\node[align=center,text width=7.0cm] at (8.4,1.25)
 {From every other original vertex:\\3 edges to an original vertex,\\then 1 more edge.};
\node[anchor=west] at (0,-.4) {(c) Reports in vertex order \(0,1,2,3,4\)};
\node[text=black] (re) at (2.7,-1.05) {$e:\ (1,1,4,4,4)$};
\node[text=black] (rf) at (9.1,-1.05) {$f:\ (1,4,1,4,4)$};
\node[draw,inner sep=5pt] (out) at (5.9,-2.0) {Same multiset \(\{1,1,4,4,4\}\)};
\draw[->] (re.south)--(out.north west);
\draw[->] (rf.south)--(out.north east);
\node[fill=white,inner sep=3pt] at (5.9,-1.32) {forget the names};
\end{tikzpicture}