Quadratic detection in linear mesoscopic transport systems produces cross terms that can be viewed as interference signals reflecting statistical properties of charge carriers. In electronic systems these cross term interferences arise from exchange effects due to Pauli principle. Here we demonstrate fermionic Hanbury Brown and Twiss (HBT) exchange phenomena due to indistinguishability of charge carriers in a diffusive graphene system. These exchange effects are verified using current-current cross correlations in combination with regular shot noise (autocorrelation) experiments at microwave frequencies. Our results can be modeled using semiclassical analysis for a square-shaped metallic diffusive conductor, including contributions from contact transparency. The experimentally determined HBT exchange factor values lie between the calculated ones for coherent and hot electron transport.