Author Summary In this work, we explore the fundamental principles underlying the architecture of the human structural connectome. We use a simple generative model that combines nonlinear preferential attachment with biologically plausible geometric constraints. This model successfully reproduces a remarkable number of brain network properties, linking the overall architecture of the brain to its underlying evolutionary principles. Additionally, we investigate the localization properties of connectome eigenmodes and identify multiple indications of their fractality. Drawing on recent advances in Anderson localization in complex systems, we conjecture that the structural connectome operates in an extended critical phase that supports multifractality.