\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);


%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) ;
\draw[thick, green] (0,1) to (0,0); 
\node[left] at (0,0.5) {$x_a$};
\draw[thick, green] (1,0) to (2,0);
\node[below]at (1.5,0) {$x_1$};
\draw[thick, green] (2,1) to (1,1); 
\node[above] at (1.5,1) {$x_a$};
\draw[thick] (2,0) to node[midway,right,scale=1,yshift=2pt]{$x_2$} (2,1);

\end{tikzpicture}

\end{document}