A standard tree-based genetic programming system, called GRNGen, for the reverse engineering of gene regulatory networks starting from time series datasets, was proposed in EvoBIO 2011. Despite the interesting results obtained on the simple IRMA network, GRNGen has some important limitations. For instance, in order to reconstruct a network with GRNGen, one single regression problem has to be solved by GP for each gene. This entails a clear limitation on the size of the networks that it can reconstruct, and this limitation is crucial, given that real genetic networks generally contain large numbers of genes. In this paper we present a new system, called GeNet, which aims at overcoming the main limitations of GRNGen, by directly evolving entire networks using graph-based genetic programming. We show that GeNet finds results that are comparable, and in some cases even better, than GRNGen on the small IRMA network, but, even more importantly (and contrarily to GRNGen), it can be applied also to larger networks. Last but not least, we show that the time series datasets found in literature do not contain a sufficient amount of information to describe the IRMA network in detail.