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Density functional theory calculations were carried out to study how the position of single-atom doping affects the electronic properties of three graphyne models. We found that the position of the dopant (B, N, or O) plays an important role in tuning the electronic structure of graphynes. For α-graphyne, the electronic structure is significantly different for different positions of B and O doping. For β-graphyne, the electronic structure depends remarkably on the doping position for O doping, but not much for B and N doping, whereas for γ-graphyne, it depends on the position for B and O doping, but not for N doping. [ABSTRACT FROM AUTHOR]