Abstract: In this paper, we study instances of complex neural networks, i.e. neural netwo rks with complex topologies. We use Self-Organizing Map neural networks whose n eighbourhood relationships are defined by a complex network, to classify handwr itten digits. We show that topology has a small impact on performance and robus tness to neuron failures, at least at long learning times. Performance may howe ver be increased (by almost $10\%$) by artificial evolution of the network topo logy. In our experimental conditions, the evolved networks are more random than their parents, but display a more heterogeneous degree distribution.