  We analyze the storage capacity of the Hopfield models on classes of random
graphs. While such a setup has been analyzed for the case that the underlying
random graph model is an Erd\"{o}s-Renyi graph, other architectures, including
those investigated in the recent neuroscience literature, have not been studied
yet. We develop a notion of storage capacity that highlights the influence of
the graph topology and give results on the storage capacity for not too
irregular random graph models. The class of models investigated includes the
popular power law graphs for some parameter values.
