From the folder containing the Python script and your matrix as a *.txt file:
$ python graphy.py your_matrix.txt
Only put the matrix in your_matrix.txt. Don't put any other LaTeX code such as \begin{matrix}.
0 & 1 & 0 \\
0 & 1/3 & 2/3 \\
1/2 & 1/2 & 0
By default, nodes are numbered starting from 1 and are placed to the right of each other. Edges are bent to the left, and loops are drawn above the node.
This script's purpose is to auto-generate a code sample for your LaTeX document. You may have to tweak it for the resulting graph to look nice.
Code generated by the script given the above matrix:
\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{automata, positioning}
\begin{document}
\begin{center}
\begin{tikzpicture}
\node[state] (1) {1};
\node[state, right=of 1] (2) {2};
\node[state, right=of 2] (3) {3};
\draw[every loop, >=latex]
(1) edge[bend left, auto=left] node {1} (2)
(2) edge[loop above] node {1/3} (2)
(2) edge[bend left, auto=left] node {2/3} (3)
(3) edge[bend left, auto=left] node {1/2} (1)
(3) edge[bend left, auto=left] node {1/2} (2);
\end{tikzpicture}
\end{center}
\end{document}After tweaking it a little bit, it looks like:
\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{automata, positioning}
\begin{document}
\begin{center}
\begin{tikzpicture}
\node[state] (1) {1};
\node[state, below left=of 1] (2) {2};
\node[state, below right=of 1] (3) {3};
\draw[every loop, >=latex]
(1) edge[bend right, auto=right] node {1} (2)
(2) edge[loop left] node {1/3} (2)
(2) edge[bend left, auto=left] node {2/3} (3)
(3) edge[bend right, auto=right] node {1/2} (1)
(3) edge[bend left, auto=left] node {1/2} (2);
\end{tikzpicture}
\end{center}
\end{document}The only changes are some left that became right and the positioning of the nodes,
yet the result is a clean Markov chain graph.