帮忙画一下马尔可夫链

Question

我需要帮助绘制一个简单的马尔可夫链。这是我使用的代码：

 \begin{tikzpicture}[
  > = stealth',
  auto,
  prob/.style = {inner sep=1pt,font=\footnotesize}
  ]
  \node[state]  (a) {$1$};
  \node[state]  (b) [right of =a]   {$2$};
  \node[state]  (c) [below right of=a,xshift=-0.5cm]    {$3$};
  \path[->] (a) edge[bend left=10] node[prob]{$1/2$} (b)
                edge[bend left=10] node[prob]{$1/2$} (c)
            (b) edge[bend left=10] node[prob]{$1/3$} (a)
                edge[bend left=10] node[prob]{$2/3$} (c)
            (c) edge[bend left=10] node[prob]{$1/3$} (a)
                edge[bend left=10] node[prob]{$2/3$} (b);           
\end{tikzpicture}

我的绘制结果是：

Answer 1

我建议使用这个简单的代码pstricks：

\documentclass{article}
\usepackage{amsmath, amssymb}
\usepackage{pst-node}

\begin{document}
\[
\begin{psmatrix}[mnode=circle, rowsep=2cm, colsep=1.2cm]
1 & & 2\\
     & 3
\end{psmatrix}
\psset{arrows=->, arrowinset=0.12, linejoin=1, labelsep=1pt, shortput=nab, arcangle=20}
\everypsbox{\scriptstyle}
\ncarc{1,1}{1,3}^{1/2} \ncarc{1,3}{1,1}^{1/2}
\psset{nrot=:U}
\ncarc{1,1}{2,2}^{1/3} \ncarc{2,2}{1,1}^{1/3}
\ncarc{1,3}{2,2}^{2/3} \ncarc{2,2}{1,3}^{2/3}
\]

\end{document} 

Answer 2

另一个 Ti钾Z 解决方案：使用automata、positioning、quotes+arrows.meta库：

\documentclass[tikz,border=3.14mm]{standalone}
\usetikzlibrary{arrows.meta, automata,
                positioning,
                quotes}

\begin{document}
    \begin{tikzpicture}[
    node distance = 29mm and 17mm,
every edge/.style = {draw, -{Stealth[scale=1.2]}, bend left=15},
every edge quotes/.append style = {auto, inner sep=2pt, font=\footnotesize}
                        ]
\node (n1)  [state] {$1$};
\node (n3)  [state,below right=of n1]   {$3$};
\node (n2)  [state,above right=of n3]   {$2$};
%
\path   (n1)    edge ["$1/2$"] (n2)
                edge ["$1/2$"] (n3)
        (n2)    edge ["$1/3$"] (n1)
                edge ["$2/3$"] (n3)
        (n3)    edge ["$1/3$"] (n1)
                edge ["$2/3$"] (n2);
    \end{tikzpicture}
\end{document}

Answer 3

您也可以使用 命令tikz-cd。

\documentclass{article}
\usepackage{tikz-cd}
\tikzcdset{arrow style=tikz, diagrams={>=stealth}}
\begin{document}
\[
\begin{tikzcd}[row sep=7em, column sep=4em, cells={nodes={draw, circle}}]
    1 \arrow[rr, bend left=15, "1/2"] \arrow[rd, bend left=15, "1/2"] & & 
    2 \arrow[ll, bend left=15, "1/3"] \arrow[ld, bend left=15, "2/3"] \\
    & 3 \arrow[lu, bend left=15, "1/3"] \arrow[ru, bend left=15, "2/3"]
\end{tikzcd}
\]
\end{document}

Answer 4

\documentclass{standalone}
\usepackage{tkz-graph}
\begin{document}
\begin{tikzpicture}[>=latex] 
 \SetGraphUnit{3}
 \Vertex {3} \NOWE(3){1}  \NOEA(3){2}
 \tikzstyle{EdgeStyle}=[->,bend left=15]   
 \tikzstyle{LabelStyle}=[fill=white] 
 \Edge[label=$1/2$](2)(1)
 \Edge[label=$1/3$](1)(2)  
 \Edge[label=$1/3$](3)(1) 
 \Edge[label=$1/3$](1)(3) 
 \Edge[label=$1/3$](3)(2) 
 \Edge[label=$2/3$](2)(3) 
\end{tikzpicture}
\end{document}