The electrochemical oxidation of adenine and guanine is studied in aqueous media using commercially available, high purity graphene which is free from surfactants and has not been chemically modified in any way, and is contrasted with edge plane pyrolytic graphite (EPPG), basal plane pyrolytic graphite (BPPG), and graphite modified electrodes. In terms of graphene modified electrodes towards the electrochemical oxidation of adenine, the observed voltammetric response is reduced, in terms of the peak height with the electrochemical oxidation potential occurring at higher oxidation potentials than the underlying BPPG electrode. In comparison, control experiments utilising graphite modified electrodes display an improvement in the voltammetric signal and reduced oxidation potentials are observed compared to the bare BPPG underlying electrode. Such a response in addition to that observed at EPPG and BPPG confirms that the density of edge plane sites are critical, which is in strong agreement with current literature reports. The reduced response at the graphene modified electrode is thus due to graphene having a low density of electroactive (edge plane) sites, given its unique structure. In the case of the electrochemical oxidation of guanine, graphene modified electrodes interestingly exhibit a lower voltammetric response in terms of peak height compared to the underlying electrode, but interestingly exhibit a reduction in the oxidation potential compared to the underlying BPPG electrode. Such a response is a consequence of the unique structure of graphene since it has a large basal plane composition for the adsorption of guanine which, according to literature reports, adsorbs readily on basal plane sites. However, graphene unfortunately has a low density of edge plane sites which accounts for the reduced voltammetric response. Additionally, pH dependence studies performed on both adenine and guanine utilising graphene modified BPPG electrodes reveal an equal number of protons and electrons transferred, suggesting graphene does not change the electrochemical mechanism prior to the chemically irreversible step compared to that observed at graphitic electrodes. Critically, the electrode surface modification with graphene is found to be analytically unacceptable; this coupled with the reduction in the overall electrode kinetics from graphene's low density of edge plane sites questions its future use in the reliable sensing of DNA bases.