  Using probabilistic approach, the transient dynamics of sparsely connected
Hopfield neural networks is studied for arbitrary degree distributions. A
recursive scheme is developed to determine the time evolution of overlap
parameters. As illustrative examples, the explicit calculations of dynamics for
networks with binomial, power-law, and uniform degree distribution are
performed. The results are good agreement with the extensive numerical
simulations. It indicates that with the same average degree, there is a gradual
improvement of network performance with increasing sharpness of its degree
distribution, and the most efficient degree distribution for global storage of
patterns is the delta function.
