Author Summary Dynamic synchronization in coupled oscillators has been studied extensively. Previously, it has been shown how these dynamics can adaptively rewire a random network structure into a complex, brain-like one. For biological and artificial networks to benefit from this dynamic self-organization, these networks must have input and memory facilities. Both functions involve breaking the symmetry of uniform network oscillators and network connectivity strength. We show that adaptive rewiring is generally robust against such perturbations. Notably, we show—via novel methods of comparing network structures—that local symmetry-breaking perturbations can develop discernible anatomical and functional connectivity structures at the global level. Our research qualifies adaptive rewiring as a potential tool for optimizing connectivity in biological and artificial neural networks. Abstract Structural plasticity of the brain can be represented in a highly simplified form as adaptive rewiring, the relay of connections according to the spontaneous dynamic synchronization in network activity. Adaptive rewiring, over time, leads from initial random networks to brain-like complex networks, that is, networks with modular small-world structures and a rich-club effect. Adaptive rewiring has only been studied, however, in networks of identical oscillators with uniform or random coupling strengths. To implement information-processing functions (e.g., stimulus selection or memory storage), it is necessary to consider symmetry-breaking perturbations of oscillator amplitudes and coupling strengths. We studied whether nonuniformities in amplitude or connection strength could operate in tandem with adaptive rewiring. Throughout network evolution, either amplitude or connection strength of a subset of oscillators was kept different from the rest. In these extreme conditions, subsets might become isolated from the rest of the network or otherwise interfere with the development of network complexity. However, whereas these subsets form distinctive structural and functional communities, they generally maintain connectivity with the rest of the network and allow the development of network complexity. Pathological development was observed only in a small proportion of the models. These results suggest that adaptive rewiring can robustly operate alongside information processing in biological and artificial neural networks.