  We studied the computational properties of an attractor neural network (ANN)
with different network topologies. Though fully connected neural networks
exhibit, in general, a good performance, they are biologically unrealistic, as
it is unlikely that natural evolution leads to such a large connectivity. We
demonstrate that, at finite temperature, the capacity to store and retrieve
binary patterns is higher for ANN with scale--free (SF) topology than for
highly random--diluted Hopfield networks with the same number of synapses. We
also show that, at zero temperature, the relative performance of the SF network
increases with increasing values of the distribution power-law exponent. Some
consequences and possible applications of our findings are discussed.
