I am trying to understand the definition of amalgamation of a $n+1$-partite graph as explained here(first few lines of page 4). We have a $n+1$-partite graph $G$ with partite sets $V_0,V_1,\cdots,V_n$ and we define amalgamation of $G$ on $V_i$ as follows: Let $W_i$ be a fixed set with $|W_i|=n|V_i|$. For each set, $A\subset W_i$ with $|A|=|V_i|$, we let $G_A$ be a "copy of G" with $i$th vertex class $V_i(G_A)=A$, all other classes disjoint. What does this mean? Classes will be disjoint for they are from different partite sets anyway.
I am trying to construct a small example as follows: Let $G$ be $K_{2,3,2}$. Suppose $V_0=\{v_1,v_2\}$, $V_1=\{w_1,w_2,w_3\}$ and $V_2=\{x_1,x_2\}$. Let $W_0=\{a_1,a_2,a_3,a_4\}$ and $A=\{a_1,a_2\}$. Now is $G_A$ the complete 3-partite graph with classes $\{a_1,a_2\},\{w_1,w_2,w_3\},\{x_1,x_2\}$?
The definition of amalgamation is as the union of all such graphs $G_A$. Does it mean the collection of all such $3$-partite graphs (visually speaking the graph obtained by drawing all such $3$-partite graphs side by side)?
Thanks for your time.