\begin{tikzpicture}[x=1cm,y=1cm,font=\small,>=Latex,
 level/.style={circle,draw=black!70,fill=none,minimum size=5.5mm,inner sep=1pt},
 component/.style={circle,draw,fill=none,minimum size=7mm,inner sep=1pt},
 acol/.style={blue!65!black,thick},
 bcol/.style={black!70,very thick},
 extra/.style={orange!85!black,very thick,densely dashed}]
\node[anchor=west] at (-.3,8.3)
 {(a) A graph of coefficient levels};
\node[anchor=west,font=\footnotesize] at (-.3,7.8)
 {For example, \((\mathcal B_1)_5=e_7-e_9\) gives the edge from \(7\) to \(9\).};
\foreach \s/\left/\right/\top/\x in {2/2/5/9/4,3/3/4/10/8,1/6/1/8/12}{
 \draw[rounded corners=3pt,fill=blue!3,draw=black!45]
   (\x-1.5,4.75) rectangle (\x+1.5,7.2);
 \node[level] (c\s) at (\x,6.65) {$\top$};
 \node[level] (l\s) at (\x-.85,5.35) {$\left$};
 \node[level] (r\s) at (\x+.85,5.35) {$\right$};
 \draw[acol] (c\s)--(l\s) (c\s)--(r\s);
 \node[inner sep=0pt] at (\x,4.43) {Star \(\s\)};
 \node[component] (v\s) at (\x,2.75) {$\s$};
 \draw[->,black!50] (\x,4.14)--(v\s.north);
}
\draw[rounded corners=3pt,fill=blue!3,draw=black!45]
 (-.2,4.75) rectangle (1.6,7.2);
\node[level] (isolated) at (.7,6.65) {$7$};
\node[inner sep=0pt] at (.7,4.43) {Isolated level};
\node[component] (v0) at (.7,2.75) {$0$};
\draw[->,black!50] (.7,4.14)--(v0.north);
\draw[bcol] (isolated)--(c2);
\node[inner sep=0pt,font=\footnotesize] at (2.05,7.01) {\((\mathcal B_1)_5\)};
\draw[extra] (r2)--(c3);
\node[inner sep=0pt,font=\footnotesize] at (6,6.43) {\((\mathcal B_1)_3\)};
\draw[bcol] (c3)--(l1);
\node[inner sep=0pt,font=\footnotesize] at (10,6.40) {\((\mathcal B_1)_4\)};
\node[align=center,font=\footnotesize] at (6,3.85) {contract\\each box};
\node[anchor=east] at (-.15,2.75) {(b)};
\draw[bcol] (v0)--(v2) node[midway,below=5pt,text=black,font=\footnotesize] {\((\mathcal B_1)_5\)};
\draw[extra] (v2)--(v3) node[midway,below=5pt,text=black,font=\footnotesize] {\((\mathcal B_1)_3\)};
\draw[bcol] (v3)--(v1) node[midway,below=5pt,text=black,font=\footnotesize] {\((\mathcal B_1)_4\)};
\node[align=center,font=\footnotesize] at (6.65,1.6)
 {The solid edges leave two components. The dashed edge joins them.};
\node[draw=black!40,rounded corners=2pt,align=center,inner sep=7pt] at (6.65,.52)
 {The shown columns connect all ten levels.\\[3pt]
 \(\rank[\mathcal A\ \mathcal B_1]\ge10-1=9
 \quad\Longrightarrow\quad \dim U_1\le6+5-9=2.\)};
\end{tikzpicture}