在 LaTex 上绘制有公共点的图形

Question

我想在 LaTex 中绘制超图，我研究了上一个问题中的代码在这个网站上并尝试修改代码来查找下面的图片，但我无法按照我想要的方式绘制超图。

Answer 1

\documentclass[tikz,border=2mm]{standalone} 
\usetikzlibrary{shapes.geometric}

\begin{document}
\begin{tikzpicture}[
    dot/.style={draw, circle, inner sep=1pt, fill=black},
    group/.style={draw=#1, ellipse, ultra thick, minimum width=4cm, minimum height=1.25cm}
    ]

    \node[dot,label=below left:$x_3$] at (0,0) (x3) {};
    \node[dot,label=below:$x_4$] at (1,0) (x4) {};
    \node[dot,label=below right:$x_5$] at (2,0) (x5) {};
    \node[dot,label=left:$x_2$] at (0.5,1) (x2) {};
    \node[dot,label=right:$x_6$] at (1.5,1) (x6) {};
    \node[dot,label=$x_1$] at (1,2) (x1) {};

    \node[group=cyan, label={[cyan]below:$E_2$}] at (x4) (E2) {};
    \node[group=olive, label={[olive]above right:$E_3$}, rotate=63] at (x2) (E3) {};
    \node[group=red, label={[red]above left:$E_1$}, rotate=-63] at (x6) (E1) {};
\end{tikzpicture}
\end{document}