如何仅通过给出顶点集和边集在 tikz 中绘制图形？

Question

正如所提到的Torbjørn T.在评论中，Ti钾Z 有一个graphdrawing库，可用于自动计算图形布局。

通过\usetikzlibrary{graphs,graphdrawing}启用图形绘图库。然后，您可以使用选择多个图形绘图库\usegdlibrary。

图形是通过给出顶点及其边来绘制的\graph。有几种方法可以做到这一点，但一种简单的方法（特别是如果图形数据是计算机生成的）是给出没有连接边的顶点，v并列出具有邻居的顶点的所有邻居v--u_1, v--u_2, ..., v--u_n。

您必须从您加载的图形绘图库中选择一个布局。（库列表可在PGF 手册，第四部分）。

可以用绘制自循环v--[loop]v，在我的测试中v--v这还不够（参见使用 tikz-graphdrawing 库进行自循环）。

您需要使用 LuaLaTeX 编译该文档，因为 graphdrawing 库依赖于 Lua 组件。（基础图是由 igraph R 包为我最近的一次研讨会演讲生成的，我只是在这个例子中添加了一个新节点 10 和 1 处的自循环。）

% !TEX TS-program = lualatex
\documentclass{article}

\usepackage{fontspec}

\usepackage{tikz}
\usetikzlibrary{graphs,graphdrawing}
\usegdlibrary{circular,force,layered,routing}

\tikzset{
  graphs/simpleer/.style={
    nodes={draw,circle, blue, left color=blue!20, text=black, inner sep=1pt},
    node distance=2.5cm, nodes={minimum size=2em}
  },
  every loop/.style={},
}

\begin{document}
  \begin{figure}
    \centering
    \begin{tikzpicture}
      \graph[simpleer, simple necklace layout]{
        1--3, 1--[loop]1,
        2--6, 5--6,
        3--7, 4--7, 5--7, 6--7,
        1--8, 6--8, 7--8,
        5--9, 6--9,
        10;
      };
    \end{tikzpicture}
    \caption{Erdős--Rényi  graph for~\(n=9\), \(p_{9}=0.3\)
      plus one loop at~\(1\)
      and an unconnected vertex~\(10\)
      drawn in \texttt{simple necklace layout}}
  \end{figure}

  \begin{figure}
    \centering
    \begin{tikzpicture}
      \graph[simpleer, layered layout]{
        1--3, 1--[loop]1,
        2--6, 5--6,
        3--7, 4--7, 5--7, 6--7,
        1--8, 6--8, 7--8,
        5--9, 6--9,
        10;
      };
    \end{tikzpicture}
    \caption{Erdős--Rényi  graph for~\(n=9\), \(p_{9}=0.3\)
      plus one loop at~\(1\)
      and an unconnected vertex~\(10\)
      drawn in \texttt{layered layout}}
  \end{figure}

  \begin{figure}
    \centering
    \begin{tikzpicture}
      \graph[simpleer, spring layout]{
        1--3, 1--[loop]1,
        2--6, 5--6,
        3--7, 4--7, 5--7, 6--7,
        1--8, 6--8, 7--8,
        5--9, 6--9,
        10;
      };
    \end{tikzpicture}
    \caption{Erdős--Rényi  graph for~\(n=9\), \(p_{9}=0.3\)
      plus one loop at~\(1\)
      and an unconnected vertex~\(10\)
      drawn in \texttt{spring layout}}
  \end{figure}
\end{document}

以下是输入图表的方法（对我来说，它看起来有点太拥挤，无法很好地绘制，但这可能是个人喜好问题）。

如果你有每个边的邻居列表，那么v -- {u_1,u_2,...,u_n},循环也必须单独列出。

% !TEX TS-program = lualatex
\documentclass{article}

\usepackage{fontspec}

\usepackage{tikz}
\usetikzlibrary{graphs,graphdrawing}
\usegdlibrary{circular}

\tikzset{
  graphs/simpleer/.style={
    nodes={draw,circle, blue, left color=blue!20, text=black, inner sep=1pt},
    nodes={minimum size=2em}
  },
  every loop/.style={},
}

\begin{document}
\begin{tikzpicture}
\graph[simpleer, simple necklace layout]{
  1 -- {1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36},
  2 -- {1,3,5,7,9,11,13,15,17,19,21,23,25,27,29,31,33,35},
  3 -- {1,2,4,5,7,8,10,11,13,14,16,17,19,20,22,23,25,26,28,29,31,32,34,35},
  4 -- {1,3,5,7,9,11,13,15,17,19,21,23,25,27,29,31,33,35},
  5 -- {1,2,3,4,6,7,8,9,11,12,13,14,16,17,18,19,21,22,23,24,26,27,28,29,31,32,33,34,36},
  6 -- {1,5,7,11,13,17,19,23,25,29,31,35},
  7 -- {1,2,3,4,5,6,8,9,10,11,12,13,15,16,17,18,19,20,22,23,24,25,26,27,29,30,31,32,33,34,36},
  8 -- {1,3,5,7,9,11,13,15,17,19,21,23,25,27,29,31,33,35},
  9 -- {1,2,4,5,7,8,10,11,13,14,16,17,19,20,22,23,25,26,28,29,31,32,34,35},
  10 -- {1,3,7,9,11,13,17,19,21,23,27,29,31,33},
  11 -- {1,2,3,4,5,6,7,8,9,10,12,13,14,15,16,17,18,19,20,21,23,24,25,26,27,28,29,30,31,32,34,35,36},
  12 -- {1,5,7,11,13,17,19,23,25,29,31,35},
  13 -- {1,2,3,4,5,6,7,8,9,10,11,12,14,15,16,17,18,19,20,21,22,23,24,25,27,28,29,30,31,32,33,34,35,36},
  14 -- {1,3,5,9,11,13,15,17,19,23,25,27,29,31,33},
  15 -- {1,2,4,7,8,11,13,14,16,17,19,22,23,26,28,29,31,32,34},
  16 -- {1,3,5,7,9,11,13,15,17,19,21,23,25,27,29,31,33,35},
  17 -- {1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,35,36},
  18 -- {1,5,7,11,13,17,19,23,25,29,31,35},
  19 -- {1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36},
  20 -- {1,3,7,9,11,13,17,19,21,23,27,29,31,33},
  21 -- {1,2,4,5,8,10,11,13,16,17,19,20,22,23,25,26,29,31,32,34},
  22 -- {1,3,5,7,9,13,15,17,19,21,23,25,27,29,31,35},
  23 -- {1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,24,25,26,27,28,29,30,31,32,33,34,35,36},
  24 -- {1,5,7,11,13,17,19,23,25,29,31,35},
  25 -- {1,2,3,4,6,7,8,9,11,12,13,14,16,17,18,19,21,22,23,24,26,27,28,29,31,32,33,34,36},
  26 -- {1,3,5,7,9,11,15,17,19,21,23,25,27,29,31,33,35},
  27 -- {1,2,4,5,7,8,10,11,13,14,16,17,19,20,22,23,25,26,28,29,31,32,34,35},
  28 -- {1,3,5,9,11,13,15,17,19,23,25,27,29,31,33},
  29 -- {1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,30,31,32,33,34,35,36},
  30 -- {1,7,11,13,17,19,23,29,31},
  31 -- {1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,32,33,34,35,36},
  32 -- {1,3,5,7,9,11,13,15,17,19,21,23,25,27,29,31,33,35},
  33 -- {1,2,4,5,7,8,10,13,14,16,17,19,20,23,25,26,28,29,31,32,34,35},
  34 -- {1,3,5,7,9,11,13,15,19,21,23,25,27,29,31,33,35},
  35 -- {1,2,3,4,6,8,9,11,12,13,16,17,18,19,22,23,24,26,27,29,31,32,33,34,36},
  36 -- {1,5,7,11,13,17,19,23,25,29,31,35},
  % loops are given separately
  1--[loop]1,
};
\end{tikzpicture}
\end{document}

Answer 1