In the development of the brain, it is known that synapses are pruned following overgrowth. This pruning
following overgrowth seems to be a universal phenomenon that occurs in almost all areas—visual cortex,
motor area, association area, and so on. It has been shown numerically that the synapse efficiency is increased
by systematic deletion. We discuss the synapse efficiency to evaluate the effect of pruning following overgrowth,
and analytically show that the synapse efficiency diverges as O(uln cu) at the limit where connecting
rate c is extremely small. Under a fixed synapse number criterion, the optimal connecting rate, which maximizes
memory performance, exists.