The climate change due to human activities stimulates the research on new energy resources. Hydrogen has attracted interest as a green carrier of high energy density. The sustainable production of hydrogen is achievable only by water electrolysis based on the hydrogen evolution reaction (HER). Graphitic materials are widely utilized in this technology in the role of conductive catalyst supports. Herein, by performing dynamic and steady-state electrochemical measurements in acidic and alkaline media, we investigated the bidirectional electrocatalysis of the HER and hydrogen oxidation reaction (HOR) on metal- and defect-free epigraphene (EG) grown on 4H silicon carbide (4H-SiC) as a ground level of structural organization of general graphitic materials. The absence of any signal degradation illustrates the high stability of EG. The experimental and theoretical investigations yield the coherent conclusion on the dominant HER pathway following the Volmer-Tafel mechanism. We ascribe the observed reactivity of EG to its interaction with the underlying SiC substrate that induces strain and electronic doping. The computed high activation energy for breaking the O-H bond is linked to the high negative overpotential of the HER. The estimated exchange current of HER/HOR on EG can be used in the evaluation of complex electrocatalytic systems based on graphite as a conducing support.