ABSTRACTThere is a one‐to‐one correspondence between the point set of a group divisible design (GDD) with groups of points and the edge set of a complete bipartite graph . A block of GDD corresponds to a subgraph of . We show that the concurrence conditions of two points of GDD can correspond to the edge concurrence conditions of subgraphs of , which we call a GDD‐type spanning bipartite block design (SBBD). We also propose a method to construct SBBD directly from an ‐design and a difference matrix over a group. When an ‐design with points has blocks much larger than , a modified method is shown to construct an SBBD with fewer blocks such that is closer to by partitioning the block set of the ‐design.