Using broken-symmetry hybrid density functional theory, we investigate the relationship between the diradical character and the second hyperpolarizabilities, gamma, for a trigonal graphene nanoflake (trigonal GNF) and two types of GNFs with rhombic and bow-tie structures composed of two trigonal GNFs. It is shown that the GNF architecture has a large impact on the diradical character and subsequently on gamma. In particular, gamma of rhombic GNF with intermediate diradical character is found to be more than twice as large as that of bow-tie GNF with nearly pure diradical character. Then, switching from the singlet to triplet state rhombic GNF exhibits a significant reduction of gamma. (C) 2009 Elsevier B. V. All rights reserved.