Please apologize: the Bratelli-Vershik graph in which I'm interested is not this one but this one:

At level $n$ there are $n$ vertices, there is one edge from each of the first $n-1$ vertices to the vertex just above at level $n-1$, and from the last vertex there are: one edge to the first vertex at level $n-1$, one edge to the second vertex, $2$ edges to the third vertex, ..., $2^{n-2}$ edges to the $(n-1)$-st vertex.

I'd like to know whether this graph induces a known example of transformation ?