Using the long-range corrected spin-unrestricted density functional theory method, the impact of antidot structure on the open-shell character and the second hyperpolarizability (γ) of graphene nanoflakes (GNFs) has been investigated for rectangular GNFs with and without antidot structure, referred to as antidot and perfect GNFs, respectively. It is found that the two GNFs exhibit different multiradical characters; the antidot GNF shows intermediate open-shell character in contrast to the perfect GNF presenting nearly pure tetraradical character. This antidot structure dependence of open-shell character can be explained in terms of their natural orbital distributions. Such difference in open-shell characters affects their γ values; the γ of the antidot GNF is about 1.7 times larger than that of the perfect GNF, the feature of which is in agreement with our previous results on the diradical character dependence of γ. © 2012 Wiley Periodicals, Inc.