Formally speaking, given two graphs: G, a D-regular graph on [N] and H, a d-regular graph on [D] - if S\subseteq[N] is a connected component of G then G|_{S} \circ H=G\circ H|_{S\times D}, where G|_{S} is the subgraph of G induced by S (i.e., the graph on S which contains all of the edges in G between vertices in S).
