  We consider the storage properties of temporal patterns, i.e. cycles of
finite lengths, in neural networks represented by (generally asymmetric) spin
glasses defined on random graphs. Inspired by the observation that dynamics on
sparse systems have more basins of attractions than the dynamics of densely
connected ones, we consider the attractors of a greedy dynamics in sparse
topologies, considered as proxy for the stored memories. We enumerate them
using numerical simulation and extend the analysis to large systems sizes using
belief propagation. We find that the logarithm of the number of such cycles is
a non monotonic function of the mean connectivity and we discuss the
similarities with biological neural networks describing the memory capacity of
the hippocampus.
