Recent studies, using unbiased sampling of neuronal activity in vivo, indicate the existence of sparse codes in the brain. These codes are characterized by highly specific, associative (i.e., dependent on combinations of features) and often invariant neuronal responses. Sparse representations present many advantages for memory storage and are, thus, of wide interest in sensory physiology. Here, we study the statistics of connectivity in an olfactory network that contributes to the generation of such codes: Kenyon cells (KCs), the intrinsic neurons of the mushroom body (a structure involved in learning and memory in insects) receive inputs from a small population of broadly tuned principal neurons; from these inputs, KCs generate exquisitely selective responses and, thus, sparse representations. We find, surprisingly, that KCs are on average each connected to about 50% of their input population. Simple analysis indicates that such connectivity indeed maximizes the difference between input vectors to KCs and helps to explain their high specificity.