  To explore the relation between network structure and function, we studied
the computational performance of Hopfield-type attractor neural nets with
regular lattice, random, small-world and scale-free topologies. The random net
is the most efficient for storage and retrieval of patterns by the entire
network. However, in the scale-free case retrieval errors are not distributed
uniformly: the portion of a pattern encoded by the subset of highly connected
nodes is more robust and efficiently recognized than the rest of the pattern.
The scale-free network thus achieves a very strong partial recognition.
Implications for brain function and social dynamics are suggestive.
