By combining phylogenetic, proteomic and structural information, we have elucidated the evolutionary driving forces for the gene-regulatory interaction networks of basic helix-loop-helix transcription factors. We infer that recurrent events of single-gene duplication and domain rearrangement repeatedly gave rise to distinct networks with almost identical hub-based topologies, and multiple activators and repressors. We thus provide the first empirical evidence for scale-free protein networks emerging through single-gene duplications, the dominant importance of molecular modularity in the bottom-up construction of complex biological entities, and the convergent evolution of networks.