Using spin-unrestricted density functional theory methods, the second hyperpolarizabilities, gamma, of rectangular graphene nanoflakes of different sizes have been investigated for their singlet ground state in conjunction with their open-shell character. It is shown that their multiradical nature leads to a unique dependence of the gamma component along the armchair edges and that this behavior can be rationalized not only in terms of the diradical character (y(0)) derived from the HOMO and LUMO occupation numbers, but also in terms of the one (y(1)) derived from the HOMO-1 and LUMO+1 ones: the gamma components are enhanced when the systems take intermediate y(1) values in addition to intermediate y(0) values. (C) 2010 Elsevier B. V. All rights reserved.