在预定义边缘之间绘制曲线

Question

我正在尝试以 LaTeX 格式绘制下图：

我的问题是如何绘制图中所示穿过节点的曲线？以及如何更改曲线左右两侧节点的颜色。谢谢！

\documentclass{article}
\usepackage{tikz}
\usepackage{verbatim}
\usepackage[active,tightpage]{preview}
\PreviewEnvironment{tikzpicture}
\setlength\PreviewBorder{5pt}%
\usetikzlibrary{arrows}

\begin{document}
\begin{tikzpicture}[>=stealth',shorten >=1pt,auto,node distance=3cm,
  thick,main node/.style={circle,fill=green!80,draw,font=\sffamily\Large\bfseries}]

  \node[main node] (1) {1};
  \node[main node] (2) [right of=1] {2};
  \node[main node] (3) [right of=2] {3};
  \node[main node] (4) [below left of=1] {4};
  \node[main node] (5) [right of=4] {5};
  \node[main node] (6) [right of=5] {6};
  \node[main node] (7) [below left of=4] {7};
  \node[main node] (8) [right of=7] {8};
  \node[main node] (9) [right of=8] {9};  
  \node[above] (10) [above of=5,node distance=6cm] {$S$};
  \node[below] (11) [below of=5,node distance=6cm] {$T$};

\begin{scope}

  \path[every node/.style={font=\sffamily\Large}]
    (1) edge node {} (4)
    (1) edge node {} (2)
    (2) edge node {} (3)
    (2) edge node {} (5)
    (3) edge node {} (6)
    (4) edge node {} (5)
    (4) edge node {} (7)
    (5) edge node {$n$} (6)
    (5) edge node {} (8)
    (6) edge node {} (9)
    (7) edge node {} (8)
    (8) edge node {} (9)
% Connect the source node with all the nodes
    (10) edge [bend left=-6] node {} (1)    
    (10) edge [bend left=20] node {} (2)
    (10) edge [bend left] node {} (3)
    (10) edge [bend right=30] node {} (4)
    (10) edge [bend right=10] node {} (5)
    (10) edge [bend left] node {} (6)
    (10) edge [bend right] node {} (7)
    (10) edge [bend right] node {} (8)
    (10) edge [bend left=20] node {} (9)
% Connect the sink node with all the nodes  
    (11) edge [bend left=10, dashed] node {} (1)    
    (11) edge [bend right=20, dashed] node {} (2)
    (11) edge [bend right, dashed] node {} (3)
    (11) edge [bend right=-20, dashed] node {} (4)
    (11) edge [bend right=5, dashed] node {} (5)
    (11) edge [bend right=20, dashed] node {} (6)
    (11) edge [bend left, dashed] node {} (7)
    (11) edge [bend right=-10, dashed] node {} (8)
    (11) edge [bend right=10, dashed] node {} (9);
\end{scope}

\end{tikzpicture}
\end{document}

Answer 1

我没有尝试优化循环作为打击乐，而只是用hobbytikzlibrary. 使用 tikzlibrary 固定线路通过的点calc。

节点颜色使用定义中的选项参数来固定main node。green将用作默认值，但可以使用main node=red选项进行更改。

\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{hobby,calc}
\usepackage{verbatim}
\usepackage[active,tightpage]{preview}
\PreviewEnvironment{tikzpicture}
\setlength\PreviewBorder{5pt}%
\usetikzlibrary{arrows}

\begin{document}
\begin{tikzpicture}[>=stealth', shorten >=1pt, auto, 
    node distance=3cm,
    thick, 
    main node/.style={circle, fill=#1!80, draw, font=\sffamily\Large\bfseries}, 
    main node/.default=green,
    Sline/.style={ultra thick, green!80!black},
    Tline/.style={ultra thick, red!80!black},
]

  \node[main node] (1) {1};
  \node[main node] (2) [right of=1] {2};
  \node[main node=red] (3) [right of=2] {3};
  \node[main node] (4) [below left of=1] {4};
  \node[main node] (5) [right of=4] {5};
  \node[main node=red] (6) [right of=5] {6};
  \node[main node] (7) [below left of=4] {7};
  \node[main node=red] (8) [right of=7] {8};
  \node[main node=red] (9) [right of=8] {9};  
  \node[above] (10) [above of=5,node distance=6cm] {$S$};
  \node[below] (11) [below of=5,node distance=6cm] {$T$};

\begin{scope}

  \path[every node/.style={font=\sffamily\Large}]
    (1) edge node {} (4)
    (1) edge node {} (2)
    (2) edge node {} (3)
    (2) edge node {} (5)
    (3) edge node {} (6)
    (4) edge node {} (5)
    (4) edge node {} (7)
    (5) edge node {$n$} (6)
    (5) edge node {} (8)
    (6) edge node {} (9)
    (7) edge node {} (8)
    (8) edge node {} (9)
% Connect the source node with all the nodes
    (10) edge [bend left=-6, Sline] node {} (1)    
    (10) edge [bend left=20, Sline] node {} (2)
    (10) edge [bend left] node {} (3)
    (10) edge [bend right=30, Sline] node {} (4)
    (10) edge [bend right=10, Sline] node {} (5)
    (10) edge [bend left] node {} (6)
    (10) edge [bend right, Sline] node {} (7)
    (10) edge [bend right] node {} (8)
    (10) edge [bend left=20] node {} (9)
% Connect the sink node with all the nodes  
    (11) edge [bend left=10, dashed] node {} (1)    
    (11) edge [bend right=20, dashed] node {} (2)
    (11) edge [bend right, dashed, Tline] node {} (3)
    (11) edge [bend right=-20, dashed] node {} (4)
    (11) edge [bend right=5, dashed] node {} (5)
    (11) edge [bend right=20, dashed, Tline] node {} (6)
    (11) edge [bend left, dashed] node {} (7)
    (11) edge [bend right=-10, dashed, Tline] node {} (8)
    (11) edge [bend right=10, dashed, Tline] node {} (9);
\end{scope}

\draw[dashed, thick, purple] (7|-11) to[curve through={($(7.center)!0.5!(8.center)$) ($(8.center)!0.5!(5.center)$) ($(5.center)!0.5!(6.center)$) ($(2.center)!0.5!(3.center)$)}] (3|-10); 
\end{tikzpicture}
\end{document}

Answer 2

一种方法是繁琐地进行大量循环

\documentclass[tikz]{standalone}
\usetikzlibrary{calc}
\begin{document}
\begin{tikzpicture}[main node/.style={circle,draw,font=\bfseries\sffamily\Large}]
\draw[thick](2.5,1.5)--++(2,3)--++(3,0)--++(-2,-3)--cycle(4,1.5) --++(2,3)(3.5,3)--++(3,0);
\foreach\x[] in{1,2,3}{
  \foreach\y[evaluate={\yi=int((\x-1)*3+\y)}] in{1,2,3}{
    \foreach\z in {1,4,5,7,8}{
      \ifnum\z=\yi\gdef\mycol{blue}\breakforeach\else\gdef\mycol{green}\fi
    }
    \node[main node,fill=\mycol!80] (\yi) at (\x + 1.5*\y,1.5*\x){\yi};
  }
}
\node[above] (10) [above of=5,node distance=6cm] {$S$};
\node[below] (11) [below of=5,node distance=6cm] {$T$};

\foreach \x in {1,...,9}{
\path (10) edge[in=90,out=-90] (\x) (\x) edge[out=-90,in=90,dashed] (11);
}
\draw[ultra thick,dotted] (2.5,0)..controls(5,5) and (4,-1)..([shift={(45:2cm)}]8.center);
\end{tikzpicture}
\end{document}