A simple method for designing efficient small-world neural networks

Small-world neural networks, as well as diluted Hopfield networks, are constructed by using matrix decomposition and a connection elimination strategy. It is shown that, to a certain extent, eliminating the unimportant synaptic couplings does not degrade the network performance. Numerical simulations give strong evidence that the small-world and diluted neural networks, by consuming a small fraction of connections, can perform as well as full-connected ones. The proposed method is simple but efficient and also potentially significant for the applications of neural circuits.