Signal noise has limited the performance and application of bioelectronics in areas such as neural interfaces and biosensors. Graphene, a two-dimensional hexagonal array of carbon atoms, shows promise as a material for bio-interface applications. This study explores the properties of graphene as a low-noise neural electrode material. Using glass-micropipette electrophysiology, signals are applied to solution-based microelectrode arrays and the response is precisely measured. Signal-to-noise ratio (SNR) is characterized and analyzed using concepts from signal theory on several material systems. These include indium-tin-oxide, various metals deposited by sputtering and inkjet printing, as well as large-area chemical vapor-deposited (CVD) graphene. Our hypothesis is that the unique chemical and electronic properties of graphene increases charge transfer and therefore lowers interfacial impedance at the biological/solid state interface. This effect is expected to be accompanied by increased SNR.