This book constitutes the thoroughly refereed post-conference proceedings of the Second International Workshop on Complex Networks, CompleNet 2010, which was held in Rio de Janeiro, Brazil, in October 2010. The 21 revised papers presented were carefully reviewed and selected from 48 submissions. The topics covered include: community structure, network metrics, network models, effect of topology to epidemics, algorithms to classify networks, self-organized algorithms applied to complex networks, as well as many applications of complex networks in biology, image analysis, software development, traffic congestion, language and speech, sensor networks, and synchronization.