¿Cómo dibujar un diagrama similar a un gráfico a continuación?

Question

\begin{center}
\begin{asy}
    unitsize(5cm);
draw(unitcircle, dashed);
    pair A1 = dir(70);
    pair A2 = dir(50);
    pair A3 = dir(10);
    pair A4 = dir(-30);
    pair A5 = dir(-60);
    pair A6 = dir(260);
    pair A7 = dir(240);
    pair A8 = dir(210);
    pair A9 = dir(135);
    label("$1$", A1, dir(A1));
    label("$2$", A2, dir(A2));
    label("$3$", A3, dir(A3));
    label("$4$", A4, dir(A4));
    label("$5$", A5, dir(A5));
    label("$6$", A6, dir(A6));
    label("$7$", A7, dir(A7));
    label("$8$", A8, dir(A8));
    label("$9$", A9, dir(A9));
    pair A = 0.3*dir(50) + 0.4*dir(80);
    pair B = 0.3*dir(50) + 0.4*dir(130);
    pair C = 0.3*dir(50) + 0.4*dir(230);
    pair D = 0.3*dir(50) + 0.4*dir(330);
    pair E = 0.3*dir(50) + 0.4*dir(20);
    \draw(A--B--C--D--E--cycle);
    \draw(A1--A--A2);
    \draw(E--A3);
    \draw(D--A4);
    pair X = B + 0.4 * dir(180);
    pair Y = C + 0.4 * dir(180);
    pair Z = Y + 0.4 * dir(245);
    pair W = D + 0.6 * dir(225);
    draw(X--A9);
    draw(Y--Z--A8);
    draw(Z--A7);
    draw(A6--W--D);
    draw(W--A5);
    draw(B--X--Y--C--W);

    dotfactor *= 2;
    dot(A, mediumgrey);
    dot(B, mediumgrey);
    dot(C, black);
    dot(D, mediumgrey);
    dot(E, black);
    dot(X, black);
    dot(Y, mediumgrey);
    dot(Z, mediumgrey);
    dot(W, black);
    
\end{asy}
\end{center}

Esta es la fotografía de Evan Chen de sus apuntes de clase.

Answer 1

Estoy más familiarizado con tikz, aquí hay una solución usando tikz. Es posible que algunas coordenadas no sean precisas, pero el código debería ser bastante sencillo. Entonces, es muy fácil modificar los nodos.

Resultado

Denominación de nodos

\documentclass{standalone}
\usepackage[T1]{fontenc}
\usepackage{expl3}
\usepackage{tikz}

\tikzset{
    plainnode/.style={
        inner sep=0pt, outer sep=0pt
    },
    graydot/.style={
        circle, fill=gray!50, minimum size=3pt, plainnode
    },
    blackdot/.style={
        circle, fill=black, minimum size=3pt, plainnode
    }
}

\ExplSyntaxOn

% set the radius of circle
\fp_new:N \l_circle_radius_fp
\fp_set:Nn \l_circle_radius_fp {2.1}
% set how much the text on the circle shifts
\fp_new:N \l_text_shift_fp
\fp_set:Nn \l_text_shift_fp {0.06}

\newcommand*{\drawcircle}{
    \node[dashed, draw, circle, inner~sep=0pt, minimum~size=\fp_eval:n{2.0 * \l_circle_radius_fp}cm] at (0, 0) {};
}

% create a new point at given location
\newcommand*{\newpoint}[4]{
    \node[#3] (#4) at (#1 cm, #2 cm) {};
}

% create a new point on the circle
\newcommand*{\newcircpoint}[3]{
    \fp_set:Nn \l_tmpa_fp {\l_circle_radius_fp*cos(#1 * \c_one_degree_fp)}
    \fp_set:Nn \l_tmpb_fp {\l_circle_radius_fp*sin(#1 * \c_one_degree_fp)}
    
    % anchor node for connecting lines
    \node[plainnode] (#2) at (\fp_use:N \l_tmpa_fp cm,\fp_use:N \l_tmpb_fp cm) {};
    
    % text node for displaying number
    \node[plainnode] at (
        \fp_eval:n {(1.0 + \l_text_shift_fp) * \l_tmpa_fp} cm, 
        \fp_eval:n {(1.0 + \l_text_shift_fp) * \l_tmpb_fp} cm) {\tiny #3};
}

% draw lines between nodes
\newcommand*{\drawline}[1]{
    \clist_set:Nn \l_tmpa_clist {#1}
    \clist_map_variable:NNn \l_tmpa_clist \l_tmpa_tl {
        \draw (\tl_item:Nn \l_tmpa_tl {1})--(\tl_item:Nn \l_tmpa_tl {2});
    }
}

\ExplSyntaxOff

\begin{document}

\begin{tikzpicture}

\drawcircle

\newpoint{-0.9}{1.2}{blackdot}{A}
\newpoint{-0.1}{1.2}{graydot}{B}
\newpoint{0.6}{1.4}{graydot}{C}
\newpoint{-0.9}{-0.1}{graydot}{D}
\newpoint{-0.1}{-0.1}{blackdot}{E}
\newpoint{1.2}{0.7}{blackdot}{F}
\newpoint{-1.2}{-1.0}{graydot}{G}
\newpoint{0.2}{-0.8}{blackdot}{H}
\newpoint{1.0}{0.0}{graydot}{I}

\newcircpoint{70}{J}{1}
\newcircpoint{55}{K}{2}
\newcircpoint{8}{L}{3}
\newcircpoint{-20}{M}{4}
\newcircpoint{-60}{N}{5}
\newcircpoint{-100}{O}{6}
\newcircpoint{-120}{P}{7}
\newcircpoint{-145}{Q}{8}
\newcircpoint{120}{R}{9}

\drawline{AB, AD, AR, BC, BE, CJ, CK, CF, DE, DG, EI, EH, FI, FL, 
    GQ, GP, HO, HN, HI, IM}

\end{tikzpicture}

\end{document}