左侧的蓝色图表中有 5 个连接。从此图表中，可以使用例如 3 个连接创建子图。总共有 10 种组合。
有没有一种聪明的方法来创建和绘制这些组合？可能是通过使用\foreach。
\documentclass[border=5pt]{standalone}
\usepackage[utf8]{inputenc}
\usepackage{amsmath}
\usepackage{tikz}
\usetikzlibrary{positioning,matrix,shapes,arrows,calc}
\begin{document}
\begin{tikzpicture}[>=stealth',auto,node distance=2cm,
thick,main node/.style={circle,draw,font=\sffamily\Large\bfseries},dashnode/.style={circle,draw,dashed,font=\sffamily\Large\bfseries}]
\node[main node,blue] at (0, 0) (1) {1};
\node[main node,blue] at (1, 1) (2) {2};
\node[main node,blue] at (1, -1) (3) {3};
\node[main node,blue] at (2, 0) (4) {4};
\draw [blue] (1) -- (2);
\draw [blue] (1) -- (3);
\draw [blue] (2) -- (4);
\draw [blue] (2) -- (3);
\draw [blue] (3) -- (4);
\node[main node] at (3, 0) (1) {1};
\node[main node] at (4, 1) (2) {2};
\node[main node] at (4, -1) (3) {3};
\node[main node] at (5, 0) (4) {4};
\foreach \k in {(1) -- (2),(2) -- (3),(2) -- (4)} {
\draw \k ;
}
\node[main node] at (6, 0) (1) {1};
\node[main node] at (7, 1) (2) {2};
\node[main node] at (7, -1) (3) {3};
\node[main node] at (8, 0) (4) {4};
\foreach \k in {(1) -- (3),(2) -- (3),(3) -- (4)} {
\draw \k ;
}
\end{tikzpicture}
\end{document}
编辑
在收到@Excelsior 的非常有帮助的评论后，问题的代码如下：
\documentclass[border=5pt]{standalone}
\usepackage[utf8]{inputenc}
\usepackage{amsmath}
\usepackage{tikz}
\usetikzlibrary{positioning,matrix,shapes,arrows,calc}
\begin{document}
% \begin{tikzpicture}[>=stealth',auto,node distance=2cm,
% thick,main node/.style={circle,draw,font=\sffamily\Large\bfseries},dashnode/.style={circle,draw,dashed,font=\sffamily\Large\bfseries}]
% \node[main node,blue] at (0, 0) (1) {1};
% \node[main node,blue] at (1, 1) (2) {2};
% \node[main node,blue] at (1, -1) (3) {3};
% \node[main node,blue] at (2, 0) (4) {4};
% \draw [blue] (1) -- (2);
% \draw [blue] (1) -- (3);
% \draw [blue] (2) -- (4);
% \draw [blue] (2) -- (3);
% \draw [blue] (3) -- (4);
% \node[main node] at (3, 0) (1) {1};
% \node[main node] at (4, 1) (2) {2};
% \node[main node] at (4, -1) (3) {3};
% \node[main node] at (5, 0) (4) {4};
% \foreach \k in {(1) -- (2),(2) -- (3),(2) -- (4)} {
% \draw \k ;
% }
% \node[main node] at (6, 0) (1) {1};
% \node[main node] at (7, 1) (2) {2};
% \node[main node] at (7, -1) (3) {3};
% \node[main node] at (8, 0) (4) {4};
% \foreach \k in {(1) -- (3),(2) -- (3),(3) -- (4)} {
% \draw \k ;
% }
% \end{tikzpicture}
\begin{tikzpicture}[
>=stealth', auto, node distance=2cm, thick,
main node/.style={circle, draw, font=\sffamily\Large\bfseries}, dashnode/.style={circle,draw,dashed,font=\sffamily\Large\bfseries}]
\node[main node,blue] at (0, 0) (1-0) {1};
\node[main node,blue] at (1, 1) (2-0) {2};
\node[main node,blue] at (1,-1) (3-0) {3};
\node[main node,blue] at (2, 0) (4-0) {4};
\draw [blue] (1-0) -- (2-0);
\draw [blue] (1-0) -- (3-0);
\draw [blue] (2-0) -- (4-0);
\draw [blue] (2-0) -- (3-0);
\draw [blue] (3-0) -- (4-0);
\foreach [evaluate=\i as \x using {3*(\i)}] \i in {1,...,11} {
\foreach \n in {1,...,4}{
\node[main node] at ($ (\n-0) + (\x,0) $) (\n-\i) {\n};
}
}
% node system 1
\foreach \k in {(1-1) -- (2-1),
(2-1) -- (3-1),
(2-1) -- (4-1)} {
\draw \k ;
}
% node system 2
\draw (1-2) -- (2-2);
\draw (2-2) -- (3-2);
\draw (3-2) -- (4-2);
\end{tikzpicture}
\end{document}
结果如下：
答案1
我尝试绘制 10 个额外的节点系统，并根据其编号进行标记。您可能最了解可能的组合，因此我将它们留空。
\documentclass[border=5pt]{standalone}
\usepackage{tikz}
\usetikzlibrary{positioning,matrix,shapes,arrows,calc}
\begin{document}
\begin{tikzpicture}[
>=stealth', auto, node distance=2cm, thick,
main node/.style={circle, draw, font=\sffamily\Large\bfseries}, dashnode/.style={circle,draw,dashed,font=\sffamily\Large\bfseries}]
\node[main node,blue] at (0, 0) (1-0) {1};
\node[main node,blue] at (1, 1) (2-0) {2};
\node[main node,blue] at (1,-1) (3-0) {3};
\node[main node,blue] at (2, 0) (4-0) {4};
\draw [blue] (1-0) -- (2-0);
\draw [blue] (1-0) -- (3-0);
\draw [blue] (2-0) -- (4-0);
\draw [blue] (2-0) -- (3-0);
\draw [blue] (3-0) -- (4-0);
\foreach [evaluate=\i as \x using {3*(\i)}] \i in {1,...,11} {
\foreach \n in {1,...,4}{
\node[main node] at ($ (\n-0) + (\x,0) $) (\n-\i) {\n};
}
}
% node system 1
\draw (1-1) -- (2-1);
\draw (2-1) -- (3-1);
\draw (2-1) -- (4-1);
% node system 2
\draw (1-2) -- (2-2);
\draw (2-2) -- (3-2);
\draw (3-2) -- (4-2);
\end{tikzpicture}
\end{document}
如果需要更多节点系统，只需增加最大值\i。
编辑
添加了可能的组合：
\documentclass[border=5pt]{standalone}
\usepackage{tikz}
\usetikzlibrary{positioning,matrix,shapes,arrows,calc}
\begin{document}
\begin{tikzpicture}[
>=stealth', auto, node distance=2cm, thick,
main node/.style={circle, draw, font=\sffamily\Large\bfseries}, dashnode/.style={circle,draw,dashed,font=\sffamily\Large\bfseries}]
\node[main node,blue] at (0, 0) (1-0) {1};
\node[main node,blue] at (1, 1) (2-0) {2};
\node[main node,blue] at (1,-1) (3-0) {3};
\node[main node,blue] at (2, 0) (4-0) {4};
\draw [blue] (1-0) -- (2-0);
\draw [blue] (1-0) -- (3-0);
\draw [blue] (2-0) -- (4-0);
\draw [blue] (2-0) -- (3-0);
\draw [blue] (3-0) -- (4-0);
\foreach [evaluate=\i as \x using {3*(\i)}] \i in {1,...,10} {
\foreach \n in {1,...,4}{
\node[main node] at ($ (\n-0) + (\x,0) $) (\n-\i) {\n};
}
}
% node system 1
\draw (1-1) -- (2-1);
\draw (2-1) -- (4-1);
\draw (2-1) -- (3-1);
% node system 2
\draw (1-2) -- (2-2);
\draw (2-2) -- (4-2);
\draw (1-2) -- (3-2);
% node system 3
\draw (1-3) -- (2-3);
\draw (2-3) -- (4-3);
\draw (3-3) -- (4-3);
% node system 4
\draw (1-4) -- (2-4);
\draw (2-4) -- (3-4);
\draw (1-4) -- (3-4);
% node system 5
\draw (1-5) -- (2-5);
\draw (2-5) -- (3-5);
\draw (3-5) -- (4-5);
% node system 6
\draw (1-6) -- (2-6);
\draw (1-6) -- (3-6);
\draw (3-6) -- (4-6);
% node system 7
\draw (1-7) -- (3-7);
\draw (2-7) -- (3-7);
\draw (3-7) -- (4-7);
% node system 8
\draw (2-8) -- (4-8);
\draw (2-8) -- (3-8);
\draw (3-8) -- (4-8);
% node system 9
\draw (2-9) -- (4-9);
\draw (2-9) -- (3-9);
\draw (1-9) -- (3-9);
% node system 10
\draw (2-10) -- (4-10);
\draw (3-10) -- (4-10);
\draw (1-10) -- (3-10);
\end{tikzpicture}
\end{document}