Coping with variations in network dosage is crucial for maintaining optimal function in gene networks. We explored how network structure facilitates network-level dosage compensation. By using the yeast galactose network as a model, we combinatorially deleted one of the two copies of its four regulatory genes and found that network activity was robust to the change in network dosage. A mathematical analysis revealed that a two-component genetic circuit with elements of opposite regulatory activity (activator and inhibitor) constitutes a minimal requirement for network-dosage invariance. Specific interaction topologies and a one-to-one interaction stoichiometry between the activating and inhibiting agents were additional essential elements facilitating dosage invariance. This mechanism of network-dosage invariance could represent a general design for gene network structure in cells.