Understanding the solution-phase dispersion of pristine, unfunctionalized graphene is important for the production of conducting inks and top-down approaches to electronics. This process can also be used as a higher-quality alternative to chemical vapor deposition. We have developed a theoretical framework that utilizes molecular dynamics simulations and the kinetic theory of colloid aggregation to elucidate the mechanism of stabilization of liquid-phase-exfoliated graphene sheets in N-methylpyrrolidone (NMP), N,N'-dimethylformamide (DMF), dimethyl sulfoxide (DMSO), gamma-butyrolactone (GBL), and water. By calculating the potential of mean force between two solvated graphene sheets using molecular dynamics (MD) simulations, we have found that the dominant barrier hindering the aggregation of graphene is the last layer of confined solvent molecules between the graphene sheets, which results from the strong affinity of the solvent molecules for graphene. The origin of the energy barrier responsible for repelling the sheets is the steric repulsions between solvent molecules and graphene before the desorption of the confined single layer of solvent. We have formulated a kinetic theory of colloid aggregation to model the aggregation of graphene sheets in the liquid phase in order to predict the stability using the potential of mean force. With only one adjustable parameter, the average collision area, which can be estimated from experimental data, our theory can describe the experimentally observed degradation of the single-layer graphene fraction in NMP. We have used these results to rank the potential solvents according to their ability to disperse pristine, unfunctionalized graphene as follows: NMP approximate to DMSO > DMF > GBL > H2O. This is consistent with the widespread use of the first three solvents for this purpose.