We have investigated the role that different connectivity regimes play on the dynamics of a network of Hodgkin-Huxley neurons by computer simulations. The different connectivity topologies exhibit the following features: random connectivity topologies give rise to fast system response yet are unable to produce coherent oscillations in the average activity of the network; on the other hand, regular connectivity topologies give rise to coherent oscillations and temporal coding, but in a temporal

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... cale that is not in accordance with fast signal processing. Finally, small-world (SW) connectivity topologies, which fall between random and regular ones, take advantage of the best features of both, giving rise to fast system response with coherent oscillations along with reproducible temporal coding on clusters of neurons. Our work is the first, to the best of our knowledge, to show the need for a small-world topology in order to obtain all these features in synergy within a biologically plausible time scale.