  We study the influence of network topology on retrieval properties of
recurrent neural networks, using replica techniques for diluted systems. The
theory is presented for a network with an arbitrary degree distribution $p(k)$
and applied to power law distributions $p(k) \sim k^{-\gamma}$, i.e. to neural
networks on scale-free graphs. A bifurcation analysis identifies phase
boundaries between the paramagnetic phase and either a retrieval phase or a
spin glass phase. Using a population dynamics algorithm, the retrieval overlap
and spin glass order parameters may be calculated throughout the phase diagram.
It is shown that there is an enhancement of the retrieval properties compared
with a Poissonian random graph. We compare our findings with simulations.
