We present a new type of self-powered, low- interference wireless sensors based on graphene circuits, which can have dual functions: chemical sensing at the molecular level and radio-frequency (RF) modulation. . We have designed two different types of circuits comprising back-gate graphene field-effect transistors (GFETs) and compared in detail their performance and implementation complexity. We have also proposed a reliable readout method based on the machine learning for extracting the mean value and the fluctuation of chemical doping levels in GFETs. We demonstrate that a fully passive, graphene-based harmonic (transponder) sensor can display a chemically sensitive frequency multiplication effect, which, when linked to a hybrid-fed small antenna, can realize an ultrasensitive, low-profile, light-weight, and potentially flexible RF sensor.