We study a new set of duality relations between weighted, combinatoric invariants of a graph G. The dualities arise from a non-linear transform $$\mathcal{B}$$ , acting on the weight function p. We define $$\mathcal{B}$$ on a space of real-valued functions $$\mathcal{O}$$ and investigate its properties. We show that three invariants (the weighted independence number, the weighted Lovasz number, and the weighted fractional packing number) are fixed points of $$\mathcal{B}^2$$ , but the weighted Shannon capacity is not. We interpret these invariants in the study of quantum non-locality.