\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,below,yshift=3pt,xshift=-3pt,scale=0.75]{ $x_\alpha$} (1,0);
\draw[gray,thick,dashed] (-0.7,1.7) to node[midway,below,scale=0.75,xshift=-2pt,yshift=2pt]{$x_\gamma$} (1,1);
\draw[gray,thick,dashed] (0,2.4) to node[midway,below,scale=0.75,xshift=-2pt,yshift=2pt]{$x_\gamma$} (1.7,1.7);
\draw[gray,thick,dashed] (0,3.4) to node[midway,above,scale=0.75,xshift=2pt,yshift=-2pt]{$x_\beta$} (1,2.4);

%snake graph outline
\draw[thick] (-0.7,1.7) to node[midway,above,xshift=-15pt, yshift=-1pt,scale=0.5]{$U_{\ell-1}x_\gamma$} (1.7,1.7);
\draw[ultra thick,white] (0,2.4) to (1,1);
\draw[thick] (0,2.4) to node[midway,xshift=14pt,yshift=-7pt,scale=0.5]{$U_{\ell+1}x_\gamma$} (1,1);
\draw[thick] (0,0) to (1,0) to node[midway,right,xshift=-2pt,scale=0.75]{$x_\gamma$} (1,1) to node[midway,below,xshift=3pt,yshift=2pt,scale=0.75]{$x_\beta$} (0,1) to (0,0);
\draw[thick] (0,1) to node[midway,below,,xshift=-1pt,scale=0.75]{$x_\alpha$} (-0.7,1.7) to node[midway,above,xshift=-4pt,scale=0.5]{$U_\ell x_\gamma$} (0,2.4) to node[midway,above,scale=0.75,yshift=-2pt]{$x_\alpha$} (1,2.4) to node[midway,right,xshift=-2pt,yshift=1pt,scale=0.75]{$x_\beta$}(1.7,1.7) to node[midway,below,scale=0.5,xshift=7pt]{$U_\ell x_\gamma$} (1,1);
\draw[thick] (0,2.4) to node[midway,left,scale=0.75,xshift=2pt]{$x_\gamma$} (0,3.4) to (1,3.4) to (1,2.4);

\end{tikzpicture}

\end{document}