\documentclass[tikz]{standalone}

\usetikzlibrary{decorations.pathreplacing,decorations.markings}
\usetikzlibrary{patterns}

\begin{document}

\begin{tikzpicture}

%diagonals + diagonal labels
\draw[gray,thick,dashed] (0,1) to node[midway,right,yshift=2pt,xshift=-2pt]{ $1$} (1,0);
\draw[gray,thick,dashed] (1,1) to node[midway,right,yshift=2pt,xshift=-2pt]{ $1$} (2,0);
\draw[gray,thick,dashed] (1,2) to node[midway,right,yshift=2pt,xshift=-2pt]{ $2$} (2,1);


%snake graph outline
\draw[thick] (0,0) to node[midway,below,scale=1,yshift=2pt]{$x_2$} (1,0) to node[midway,right,xshift=-3pt,yshift=-8pt]{$\mu x_1$} (1,1) to node[midway,above,xshift=-1pt,yshift=-2pt]{$x_1$} (0,1) to node[midway,left,xshift=2pt]{$x_a$}(0,0);
\draw[thick] (1,0) to node[midway,below,yshift=2pt]{$x_1$} (2,0) to node[midway,right,xshift=-2pt]{$x_2$} (2,1);
\draw[thick] (1,2) to node[midway,above,yshift=-1pt]{} (2,2) to node[midway,right,xshift=-1pt]{} (2,1) to node[midway,above,yshift=-2pt]{$x_a$} (1,1) to node[midway,left,xshift=3pt]{$x_1$} (1,2);

\end{tikzpicture}

\end{document}