\documentclass[tikz]{standalone}

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

\begin{document}

\begin{tikzpicture}

%diagonals + diagonal labels
\draw[gray,thick,dashed] (0,2) to node[midway,right,yshift=2pt,xshift=-2pt]{ $1$} (1,1);
\draw[gray,thick,dashed] (0,3) to node[midway,right,yshift=2pt,xshift=-2pt]{ $1$} (1,2);
\draw[gray,thick,dashed] (0,4) to node[midway,right,yshift=2pt,xshift=-2pt]{ $2$} (1,3);


%snake graph outline
\draw[thick] (0,1) to node[midway,left,scale=1,xshift=1pt]{$x_a$} (0,2) to node[midway,above,scale=1,xshift=-3pt,yshift=-4pt]{$\mu x_1$}  (1,2) to node[midway,right,scale=1,xshift=-2pt]{$x_1$}  (1,1) to node[midway,below,scale=1,xshift=1pt,yshift=2pt]{$x_2$} (0,1);
\draw[thick] (1,2) to node[midway,right,scale=1,yshift=-1pt,xshift=-2pt]{$x_2$}  (1,3) to node[midway,above,scale=1,xshift=-1pt,yshift=-2pt]{$x_a$}  (0,3) to node[midway,left,scale=1,xshift=2pt]{$x_1$} (0,2);
\draw[thick] (0,3) to node[midway,left,scale=1,xshift=2pt]{$x_1$} (0,4) to (1,4) to (1,3);


\end{tikzpicture}

\end{document}