  The standard notion of NS-NS 3-form flux is lifted to Hitchin's generalized geometry. This generalized flux is given in terms of an integral of a modified Nijenhuis operator over a generalized 3-cycle. Explicitly evaluating the generalized flux in a number of familiar examples, we show that it can compute three-form flux, geometric flux and non-geometric Q-flux. Finally, a generalized connection that acts on generalized vectors is described and we show how the flux arises from it. 
NS-NS fluxes in Hitchin's generalized geometry