绘制图形：使用（x，y）坐标而不是角度来确定顶点的位置

Question 1

这Sandy G 的回答已经回答了您的初始问题，但我想提供另一种使用 TikZ 绘制图片的方法。该密钥decide color可能也适用于其他答案，因为您不需要在列表中隐式指定颜色。

在LuaLaTeX的支持下我们可以使用TikZgraphdrawing及其force库。

这force图书馆（）规定\usegdlibrary{force}spring electrical layout。

这graphs图书馆（）规定\usetikzlibrary{graphs}typeset钥匙用于定义依赖于节点名称的节点文本。

此名称还将用于decide color应用适当的颜色样式：

decide color/.style 2 args={
  /utils/TeX if=c#1
    {% if the first letter is c
     % and the number after is is smaller than 5 → bluelight
     %                                 otherwise → bluedark
      /utils/if={#2<5}{bluelight}{bluedark}
    }{% if the first letter is not c (i.e. p)
      % and the number after it is smaller than 8 → light
      %                                 otherwuse → dark
      /utils/if={#2<8}{light}{dark}
    }
}

代码

% arara: lualatex
\documentclass[tikz]{standalone}
\usetikzlibrary{graphs,graphdrawing}
\usegdlibrary{force}
\makeatletter
\pgfkeys{
  /utils/if/.code n args={3}{%
  \pgfmathparse{#1}\ifdim\pgfmathresult pt=0pt\relax
    \expandafter\pgfutil@firstoftwo\else\expandafter\pgfutil@secondoftwo\fi
    {\pgfkeysalso{#3}}{\pgfkeysalso{#2}}},
  /utils/TeX if/.code n args={4}{%
    \if#1#2\expandafter\pgfutil@firstoftwo\else\expandafter\pgfutil@secondoftwo\fi
    {\pgfkeysalso{#3}}{\pgfkeysalso{#4}}}}
\makeatother
\tikzset{
  mynode/.style={
    circle, minimum size=10mm, draw, densely dashdotted, thick,
    decide color/.expand once=#1},
  decide color/.style 2 args={
    /utils/TeX if=c#1% c1-c4 / c5- / ?1-?7 / ?8-
      {/utils/if={#2<5}{bluelight}{bluedark}}
      {/utils/if={#2<8}{light}{dark}}},
  light/.style={fill=gray!20},  bluelight/.style={fill=blue!10},
  dark/.style ={fill=gray!60},  bluedark/.style ={fill=blue!30}}
\begin{document}
\tikz\graph[
  spring electrical layout, horizontal=c2 to p13,
  node distance=1.5cm, typeset=$n_{\tikzgraphnodetext}$,
  nodes={mynode=\tikzgraphnodetext}] {
  % outer ring
  c2 -- {p1, p11, p6};
    p1 -- {p8, c6, p11};
      p8 -- {p3, p10, c6};
       p3 -- {p13, p15, p10};
         p13 -- {p15, c7};
           c7  -- {c3, c4, p15};
           c3  -- {p14, c4};
           p14 -- {p7, c4};
         p7 -- {p9, p2, c4};
       p9 -- {c5, p12, p2};
     c5 -- {c1, p4, p12};
   c1 -- {p6, p4};
  p6 -- {p11, p4};
  % inner ring
  p11 -- {c6, p12, p4};
  p5 -- {c6 -- {p10, p12}, p10 -- p15, p15 -- c4, c4 -- p2, p2 -- p12, p12 -- p4};
  % last line is equivalent to:
  % c6 -- {p10, p5, p12}; p10 -- {p15, p5}; p15 -- {c4, p5};
  % c4 -- {p2, p5};       p2  -- {p12, p5}; p12 -- {p4, p5};
};
\end{document}

输出

Answer