\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);
\draw[gray,thick,dashed] (2,2) to node[midway,right,yshift=2pt,xshift=-2pt]{ $2$} (3,1);



%snake graph outline
\draw[thick] (0,0) to (1,0) ;
\node [below,scale=1,yshift=-2pt] at (0.5,0) {$x_2$};
\draw[thick] (1,0)to node[midway,right ,scale=1,yshift=-7pt, xshift = -2pt]{$\mu x_1$} (1,1);
\node [above,scale=1,yshift=-2pt] at (0.5,1) {$x_1$};
\draw[thick] (1,1) to  (0,1) ;
\draw[thick] (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) ;
\draw[thick] (2,0) to (2,1);
\node [right ,scale=1,yshift=-2pt] at (2,0.5) {$x_2$};
\draw[thick] (1,2) to  (2,2);
\node [above] at (1.5,2) {$x_2$};
\draw (2,2) to node[midway,right,yshift=-7pt]{$\lambda x_2$} (2,1) to node[midway,above,yshift=-2pt]{$x_a$} (1,1) to node[midway,left,xshift=3pt]{$x_1$} (1,2);
\draw[thick] (3,1) to (3,2); 
\node [right,scale=1,yshift=-2pt] at (3,1.5) {$x_a$};
\draw[thick] (2,1) to node[midway,below,xshift=-1pt]{$x_2$} (3,1);
\draw[thick](2,2) to node[midway,above,xshift=-1pt]{$x_1$}(3,2);

\draw[gray,thick,dashed] (5,1) to node[midway,right,yshift=2pt,xshift=-2pt]{ $1$} (6,0);
\draw[gray,thick,dashed] (6,1) to node[midway,right,yshift=2pt,xshift=-2pt]{ $1$} (7,0);
\draw[gray,thick,dashed] (6,2) to node[midway,right,yshift=2pt,xshift=-2pt]{ $2$} (7,1);

\draw[thick] (5,0) to (6,0) ;
\node [below,scale=1,yshift=-2pt] at (5.5,0) {$x_2$};
\draw[thick] (6,0)to node[midway,right ,scale=1,yshift=-7pt, xshift = -2pt]{$\mu x_1$} (6,1);
\node [above,scale=1,yshift=-2pt] at (5.5,1) {$x_1$};
\draw[thick] (6,1) to  (5,1) ;
\draw[thick] (5,1) to node[midway,left,xshift=2pt]{$x_a$}(5,0);
\draw[thick] (6,0) to node[midway,below,yshift=2pt]{$x_1$} (7,0) ;
\draw[thick] (7,0) to (7,1);
\node [right ,scale=1,yshift=-2pt] at (7,0.5) {$x_2$};
\draw[thick] (7,2) to  (6,2);
\node [above] at (6.5,2) {};
\draw (7,2) to node[midway,right,yshift=-7pt]{} (7,1) to node[midway,above,yshift=-2pt]{$x_a$} (6,1) to node[midway,left,xshift=3pt]{$x_1$} (6,2);

\node[] at (4,1){$=$};
\node[] at (8,1){$\bigoplus$};

\draw[gray,thick,dashed] (9,1) to node[midway,right,yshift=2pt,xshift=-2pt]{ $1$} (10,0);
\draw[gray,thick,dashed] (9,2) to node[midway,right,yshift=2pt,xshift=-2pt]{ $2$} (10,1);
\draw[gray,thick,dashed] (10,2) to node[midway,right,yshift=2pt,xshift=-2pt]{ $2$} (11,1);

\draw[thick] (9,1) to (9,0)to (10,0);
\draw[thick] (10,1) to node[midway, above]{$x_a$}  (9,1) ;
\draw[thick] (9,1) to node[midway,left,xshift=2pt]{}(9,0);
\draw[thick] (9,1) to node[midway,left,yshift=2pt]{$x_1$} (9,2) ;
\draw[thick] (9,2) to node[midway, above, yshift = -2pt] {$x_2$} (10,2);
\draw[thick] (11,2) to node[midway, above, yshift = -2pt]{$x_1$} (10,2);
\node [above] at (10.5,2) {};
\draw (11,2) to node[midway,right, xshift = -2pt]{$x_a$} (11,1) to node[midway,below,yshift=-2pt]{$x_2$} (10,1) to node[midway,right,yshift=-6pt]{$\lambda x_2$} (10,2);
\draw[thick](10,0) to node[midway, right]{$x_2$} (10,1);

\end{tikzpicture}



\end{document}