\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!65,fill=white,inner sep=0pt,minimum size=3.5pt}]
\node[anchor=west] at (0,4.1) {(a) Replacing one edge of \(K_5\)};
\node[anchor=west] at (6.7,4.1) {(b) Measuring from \(W=\{s_1,s_2,s_3\}\)};
\foreach \L/\yy in {2/3.25,3/2.1,5/.95}{
 \node[anchor=east] at (.65,\yy) {\(L=\L\)};
 \coordinate (left\L) at (1.05,\yy);
 \coordinate (right\L) at (5.2,\yy);
 \draw (left\L)--(right\L);
 \node[original,label=above:\(u\)] at (left\L) {};
 \node[original,label=above:\(v\)] at (right\L) {};
 \pgfmathtruncatemacro{\last}{\L-1}
 \foreach \j in {1,...,\last}{
  \node[internal] at ($(left\L)!\j/\L!(right\L)$) {};
 }
}
\node[align=center] at (3.1,.15) {\(L\) edges, \(L-1\) new vertices};
\foreach \j in {0,...,5}{\coordinate (p\j) at ({7.05+.9*\j},2.1);}
\draw (p0)--(p5);
\draw[blue!70!black,line width=1.8pt] (p2)--(p3);
\foreach \j in {1,...,4}{\node[internal] at (p\j) {};}
\node[original] at (p0) {};
\node[original] at (p5) {};
\foreach \j in {0,1,5}
 {\draw[blue!70!black,line width=.8pt] (p\j) circle[radius=4.2pt];}
\node[below=6pt] at (p0) {\(s_1\)};
\node[below=6pt] at (p1) {\(s_2\)};
\node[below=6pt] at (p5) {\(s_3\)};
\node[below=6pt] at (p2) {\(x\)};
\node[below=6pt] at (p3) {\(y\)};
\node[above=4pt] at ($(p2)!.5!(p3)$) {\(e\)};
\draw[decorate,decoration={brace,amplitude=5pt}]
 (7.05,2.55)--(8.85,2.55)
 node[midway,above=7pt] {\(d(x,s_1)=2\)};
\draw[decorate,decoration={brace,mirror,amplitude=5pt}]
 (7.05,1.3)--(9.75,1.3)
 node[midway,below=7pt] {\(d(y,s_1)=3\)};
\node at (9.25,.05) {\(d(e,s_1)=\min\{2,3\}=2\)};
\node[draw,inner sep=5pt] at (9.25,-.65)
 {Distance multiset: \(\{1,2,2\}\)};
\node[anchor=west] at (10.4,3.25) {\(L=5\)};
\end{tikzpicture}