\documentclass[tikz]{standalone}

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

\begin{document}

\begin{tikzpicture}[scale = 1.3]

%diagonals + diagonal labels
\draw[gray,thick,dashed] (0,1) to node[midway,below,yshift=3pt,xshift=-3pt,scale=0.75]{ $x_\alpha$} (1,0);
\draw[gray,thick,dashed] (0,2) to node[midway,below,yshift=3pt,xshift=-3pt,scale=0.75]{ $x_\ell$} (1,1);
\draw[gray,thick,dashed] (1,2) to node[midway,below,yshift=3pt,xshift=-3pt,scale=0.75]{ $x_r$} (2,1);
\draw[gray,thick,dashed] (2,2) to node[midway,below,yshift=3pt,xshift=-3pt,scale=0.75]{ $x_r$} (3,1);
\draw[gray,thick,dashed] (3,2) to node[midway,below,yshift=3pt,xshift=-3pt,scale=0.75]{ $x_\ell$} (4,1);
\draw[gray,thick,dashed] (4,2) to node[midway,below,yshift=3pt,xshift=-3pt,scale=0.75]{ $x_\beta$} (5,1);

%snake graph outline
\draw[thick] (0,0) to (1,0);
\draw[thick, orange] (1,0) to node[midway,right,xshift=-2pt,scale=0.75]{$x_\ell$} (1,1);
\draw[thick] (1,1) to node[midway,below,xshift=3pt,yshift=2pt,scale=0.75]{$x_\beta$} (0,1);
\draw[thick, orange] (0,1) to (0,0);
\draw[thick] (0,1) to node[midway,left,scale=0.75]{$x_\alpha$}  (0,2);
\draw[thick, orange] (0,2) to node[midway,above,scale=0.75]{$x_r$} (1,2);
\draw[thick] (1,2) to node[midway,right,xshift=-2pt,scale=0.75]{$x_r$} (1,1);
\draw[thick] (1,2) to node[midway,above,scale=0.75]{$x_r$} (2,2);
\draw[thick, orange] (2,2) to node[midway,right, xshift=-2pt, scale=0.75]{$x_\ell$} (2,1);
\draw[thick] (2,1) to node[midway,below,scale = 0.75] {$x_\ell$} (1,1);
\draw[thick] (2,2) to node[midway,above,scale=0.75]{$x_\ell$} (3,2);
\draw[thick, orange] (3,2) to node[midway,right, scale=0.75, xshift=-2pt]{$x_r$} (3,1);
\draw[thick] (3,1) to node[midway,below,scale = 0.75] {$x_r$} (2,1);
\draw[thick] (3,2) to node[midway,above,scale=0.75]{$x_\alpha$} (4,2);
\draw[thick, orange] (4,2) to node[midway,right, xshift = -2, scale=0.75]{$x_\beta$} (4,1);
\draw[thick] (4,1) to node[midway,below,scale = 0.75] {$x_r$} (3,1);
\draw[thick](4,2) to (5,2);
\draw[thick, orange] (5,2) to (5,1);
\draw[thick] (5,1)to node[midway, below, scale = 0.75] {$x_\rho$} (4,1);

\end{tikzpicture}

\end{document}