  A neural network works as an associative memory device if it has large
storage capacity and the quality of the retrieval is good enough. The learning
and attractor abilities of the network both can be measured by the mutual
information (MI), between patterns and retrieval states. This paper deals with
a search for an optimal topology, of a Hebb network, in the sense of the
maximal MI. We use small-world topology. The connectivity $\gamma$ ranges from
an extremely diluted to the fully connected network; the randomness $\omega$
ranges from purely local to completely random neighbors. It is found that,
while stability implies an optimal $MI(\gamma,\omega)$ at
$\gamma_{opt}(\omega)\to 0$, for the dynamics, the optimal topology holds at
certain $\gamma_{opt}>0$ whenever $0\leq\omega<0.3$.
