A method is presented to prepare high concentration graphene dispersions (up to 1.2 mg/ml) with yields of up to 4 wt% monolayers. The process involves long-time low-power sonication (up to 460 hours) in N-methyl-pyrrolidone (NMP). TEM analysis shows flake dimensions scale as t^(-1/2), while the mean flake length remains above 1 µm. Raman spectroscopy indicates edge defects rather than basal-plane defects are introduced. These dispersions can be heavily diluted with water without sedimentation or aggregation, enabling the preparation of high-quality free-standing graphene films with reasonable electrical and mechanical properties. The method allows for high concentration graphene processing for various applications. The concentration of graphene increases with sonication time, following a square root relationship. Centrifugation at higher rates reduces concentration, but the system remains close to a critical concentration similar to polymer physics overlap concentration. The observed Raman D/G band intensity ratio increases with sonication time, indicating new edges rather than basal-plane defects. Aqueous dilution of NMP dispersions shows minimal aggregation or sedimentation, allowing the formation of free-standing films with good mechanical and electrical properties. This method facilitates the preparation of materials such as composites or transparent films.A method is presented to prepare high concentration graphene dispersions (up to 1.2 mg/ml) with yields of up to 4 wt% monolayers. The process involves long-time low-power sonication (up to 460 hours) in N-methyl-pyrrolidone (NMP). TEM analysis shows flake dimensions scale as t^(-1/2), while the mean flake length remains above 1 µm. Raman spectroscopy indicates edge defects rather than basal-plane defects are introduced. These dispersions can be heavily diluted with water without sedimentation or aggregation, enabling the preparation of high-quality free-standing graphene films with reasonable electrical and mechanical properties. The method allows for high concentration graphene processing for various applications. The concentration of graphene increases with sonication time, following a square root relationship. Centrifugation at higher rates reduces concentration, but the system remains close to a critical concentration similar to polymer physics overlap concentration. The observed Raman D/G band intensity ratio increases with sonication time, indicating new edges rather than basal-plane defects. Aqueous dilution of NMP dispersions shows minimal aggregation or sedimentation, allowing the formation of free-standing films with good mechanical and electrical properties. This method facilitates the preparation of materials such as composites or transparent films.