I would like to be able to draw this image in LaTeX but have no idea how to do so. I am new to graphs in LaTeX so any help would be much appreciated.
The red, green and blue circles along with annotations are not part of the image; they are there to explain length requirements. Also, the final graph produced need not follow that same format. As long as all the lines are drawn, I would be able to work out the positioning.
It is also a proper subset symbol, not a C. Thank you in advance.
Edit: I figured it out after the suggestion to use Tikz (thank you @SebGlav).
\begin{center}
\begin{tikzpicture}[scale=1.5]
\node (a) at (0,0) [fill,circle,inner sep=1.2pt] {};
\node (b) at (1,0) [fill,circle,inner sep=1.2pt] {};
\node (c) at (4,0) [fill,circle,inner sep=1.2pt] {};
\node (d) at (5,0) [fill,circle,inner sep=1.2pt] {};
\draw (0,0) -- (1,0) -- (4,0) -- (5,0);
\draw [gray,decorate,decoration={brace,amplitude=5pt},
xshift=0pt,yshift=-4pt]
(1,0) -- (0,0)
node [black,midway,below=4pt,xshift=0pt]
{\footnotesize $I_1$};
\draw [gray,decorate,decoration={brace,amplitude=5pt},
xshift=0pt,yshift=-4pt]
(4,0) -- (1,0)
node [black,midway,below=4pt,xshift=0pt]
{\footnotesize $I_2$};
\draw [gray,decorate,decoration={brace,amplitude=5pt},
xshift=0pt,yshift=-4pt]
(5,0) -- (4,0)
node [black,midway,below=4pt,xshift=0pt]
{\footnotesize $I_3$};
\end{tikzpicture}
\bigskip
\begin{tikzpicture}[scale=1.5]
\node (a) at (0,0) [fill,circle,inner sep=1.2pt] {};
\node (b) at (2,0) [fill,circle,inner sep=1.2pt] {};
\node (c) at (3,0) [fill,circle,inner sep=1.2pt] {};
\node (d) at (5,0) [fill,circle,inner sep=1.2pt] {};
\draw (0,0) -- (1,0) -- (4,0) -- (5,0);
\draw [gray,decorate,decoration={brace,amplitude=5pt},
xshift=0pt,yshift=-4pt]
(2,0) -- (0,0)
node [black,midway,below=4pt,xshift=0pt]
{\footnotesize $I'_1$};
\draw [gray,decorate,decoration={brace,amplitude=5pt},
xshift=0pt,yshift=-4pt]
(3,0) -- (2,0)
node [black,midway,below=4pt,xshift=0pt]
{\footnotesize $I'_2$};
\draw [gray,decorate,decoration={brace,amplitude=5pt},
xshift=0pt,yshift=-4pt]
(5,0) -- (3,0)
node [black,midway,below=4pt,xshift=0pt]
{\footnotesize $I'_3$};
\end{tikzpicture}
\end{center}