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如何绘制每个顶点和中心枢纽之间有双直边的图形

tag-icon • tag-icon tikz-pgf tikz-graphs
如何绘制每个顶点和中心枢纽之间有双直边的图形

我想制作这个图表。我在 PGF 手册中找到了几个类似的内容，但我找不到绘制的方法：

  1. 中心枢纽/节点（顶点）
  2. 直双边（即双线/箭头）

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以下是我根据手册尝试的一些操作，但它们并不接近：

\documentclass[10pt]{article}
\usepackage{tikz}
\usepackage{pgfplots}
\pgfplotsset{compat=1.16}
\usetikzlibrary{arrows.meta}
\usetikzlibrary{graphs}
\usetikzlibrary{graphs.standard}

\begin{document}%%

\tikz \graph [clockwise=6]       { a, b, c, d, e, f  [<->]}; 
\tikz \graph [clockwise=6,clique]{ a, b, c, d, e, f  [<->]}; 
\tikz \graph [clockwise]         { subgraph I_n [n=6,<->] }; 
\tikz \graph [clockwise,clique]  { subgraph I_n [n=6,<->] }; 
\tikz \graph [clockwise]         { subgraph K_n [n=6,<->] }; \\
\tikz \graph [clockwise,clique]  { subgraph K_n [n=6,<->] }; 
\tikz \graph [clockwise]         { subgraph C_n [n=6,<->] }; 
\tikz \graph [clockwise,clique]  { subgraph C_n [n=6,<->] }; 
\tikz \graph [clockwise]         { subgraph P_n [n=6,<->] }; 
\tikz \graph [clockwise=6,multi] {{ a, b, c, d, e, f };
a <->[bend left] b;
a <->[bend right] b; 
b <->[bend left] c;
b <->[bend right] c; 
c <->[bend left] d;
c <->[bend right] d; 
d <->[bend left] e;
d <->[bend right] e; 
e <->[bend left] f;
e <->[bend right] f; 
f <->[bend left] a;
f <->[bend right] a; 
};    

%\tikz \graph [spring electrical layout, horizontal=0 to 1] { 0 [electric charge=1] -- subgraph C_n [n=6] }; 
% ^^^ couldn't get this one to work at all for some reason

\end{document}%%

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答案1

tikz使用简单的calc库进行箭头定位：

在此处输入图片描述

\documentclass[tikz, margin=3mm]{standalone}
\usetikzlibrary{arrows.meta,
                calc}

\begin{document}
    \begin{tikzpicture}[
every node/.style = {circle, draw, minimum size=2em},
       arr/.style = {Stealth-Stealth, semithick, shorten <=#1, shorten >=#1},
                        ]
\node (c)  {};
    \foreach \i [count=\j from 0] in {A,...,F}
\node (n\j) at (150-\j*60:24mm) {\i};
%
    \foreach \i in {0,1,...,5}
{
\draw[arr=1em] ($(c)!1mm!90:(n\i)$) -- ($(n\i)!1mm!-90:(c)$);
\draw[arr=1em] ($(c)!1mm!-90:(n\i)$) -- ($(n\i)!1mm!90:(c)$);
}
   \end{tikzpicture}
\end{document}
  • 使用极坐标来定位节点（在循环中）
  • 确定箭头的坐标时，使用calc包提供的部分修饰符语法。此坐标计算在 TikZ \& PGF 手册第 146-147 页中有描述：
($(start coordinate)!distance!angle:(end coordinate)$)

(start coordinate)其中坐标从垂直线偏移distance（即偏移角为 90 度）(start coordinate) -- (end coordinate)

答案2

图形布局很简单，pgfmanual 第 269 页的第二个示例中已经介绍过（当然已C_n替换为I_n）。如果路径是直的，则两个平行箭头可以很容易地以某种样式投射。

\documentclass[tikz,border=3.14mm]{standalone}
\usetikzlibrary{graphs,graphs.standard}
\usetikzlibrary{decorations.pathreplacing,calc}
\tikzset{two parallel arrows/.style={decorate,decoration={show path construction,
      lineto code={
       \draw [stealth-stealth] ($(\tikzinputsegmentfirst)!#1!90:(\tikzinputsegmentlast)$) 
        -- ($(\tikzinputsegmentlast)!#1!-90:(\tikzinputsegmentfirst)$); 
       \draw [stealth-stealth] ($(\tikzinputsegmentfirst)!#1!-90:(\tikzinputsegmentlast)$) 
        -- ($(\tikzinputsegmentlast)!#1!90:(\tikzinputsegmentfirst)$); 
      }}},two parallel arrows/.default=3pt}
\begin{document}
\begin{tikzpicture}
\graph  [nodes={draw, circle,inner sep=1em,font=\sffamily},radius=2cm] 
{ subgraph I_n [n=6, clockwise,name=outer,V={A,B,C,D,E,F}]  
--[shorten <=1pt, shorten >=1pt,
two parallel arrows]  {a} };
\end{tikzpicture}

\begin{tikzpicture}
\graph [nodes={draw, circle,inner sep=1em,font=\sffamily}, 
clockwise, radius=1.5cm] {
subgraph I_n [name=inner, n=1,radius=0cm,/tikz/text opacity=0] 
--[shorten <=1pt, shorten >=1pt,two parallel arrows]
subgraph I_n [name=outer, n=6,V={A,B,C,D,E,F}] };
\end{tikzpicture}
\end{document}

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如果你还考虑弯曲路径，你可以使用这个答案因为它也允许您将它们用于弯曲的箭头。

\documentclass[tikz,border=3.14mm]{standalone}
\usetikzlibrary{graphs,graphs.standard,arrows.meta}
\makeatletter
\pgfkeys{ % from https://tex.stackexchange.com/a/232468/121799
  /pgf/arrow keys/.cd,
  Bidirectional/.style={
    length = +1.05pt 1.925 1,
    shear
  },
  shear/.code={
    \pgfarrowsthreeparameters{#1}%
    \expandafter\pgfarrowsaddtooptions\expandafter{\expandafter\pgfarrowslinewidthdependentnew\pgfarrowstheparameters\pgfarrowshear\pgf@x}%
  },
  shear/.default = +0pt -.5 -.5
}
\newdimen\pgfarrowshear
\pgfarrowshear0pt
\def\pgfarrowslinewidthdependentnew#1#2#3{%
  \pgf@x#1%
  \ifdim\pgfinnerlinewidth>0pt%
    \pgf@arrows@inner@line@width@depnew{#2}{#3}%
  \else%  
    \advance\pgf@x by#2\pgflinewidth%
  \fi%
}
\def\pgf@arrows@inner@line@width@depnew#1#2{%
  % #1 * outer line width + #2 * inner line width = our new one = the following
  % (#1/2) * full line width + (#2-#1/2) * inner line width)
  % Compute "real" line width
  \[email protected]\pgflinewidth%
  \pgf@xa#1\pgf@xa%
  \advance\pgf@x by\pgf@xa%
  \pgf@xa\pgfinnerlinewidth%
  \[email protected]\pgf@xa%
  \advance\pgf@x by#2\pgf@xa%
  \advance\pgf@x by-#1\pgf@xb%
}
\def\pgf@arrow@drawer@shift#1#2#3{
  \pgftransformyshift\pgfarrowshear%
  \pgf@xb#2\pgftransformxshift{-\pgf@xb}%
  \pgf@xc#1%
  \advance\pgf@xc by\pgfarrowsep%
  \advance\pgf@xc by-\pgf@xb%
}
\makeatother
\begin{document}
\begin{tikzpicture}[bidi/.style={thick,double,double
distance=3pt,{<[Bidirectional]}-{>[Bidirectional]}}]
\graph  [nodes={draw, circle,inner sep=1em},empty nodes,radius=2cm] 
{ subgraph I_n [n=6, clockwise,name=outer] --[bidi,shorten <=1pt, shorten >=1pt] {a} };
\end{tikzpicture}
\end{document}

在此处输入图片描述

答案3

\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{automata,arrows,calc,positioning}

\begin{document}

\begin{tikzpicture}[>=stealth',shorten >=1pt,auto,node distance=1.5cm and 4cm,scale=1, transform shape,align=center,minimum size=3em]

    \node[state]    (E)                              {E};  
    \node[state]    (B)    [right=of E]              {B};
    \node[state]    (A)    [above=of $(E)!0.5!(B)$]  {A};
    \node[state,xshift=-0.6cm]    (C)    [below=of B]              {C};
    \node[state,xshift=0.6cm]    (D)    [below=of E]              {D};
    \node[state]    (F)    [below=of A]              {};

    \draw[double distance=5pt] 
    (F) -- (A) 
    (F) -- (B)
        (F) -- (C)
        (F) -- (D)
        (F) -- (E);

\end{tikzpicture}


\end{document}

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