Electrical double layer (EDL) capacitors based on recently emergent graphene materials have shown several folds performance improvement compared to conventional porous carbon materials, driving a wave of technology breakthrough in portable and renewable energy storage. Accordingly, much interest has been generated to pursue a comprehensive understanding of the fundamental yet elusive double layer structure at the electrode/electrolyte interface. In this paper, we carried out comprehensive molecular dynamics simulations to obtain a comprehensive picture of how ion type, solvent properties, and charging conditions affect the EDL structure at the graphene electrode surface, and thereby its contribution to capacitance. We show that different symmetrical monovalent aqueous electrolytes M⁺X^– (M⁺ = Na⁺, K⁺, Rb⁺, and Cs⁺; X^– = F^–, Cl^–, and I^–) indeed have distinctive EDL structures. Larger ions, such as, Rb⁺, Cs⁺, Cl^–, and I^–, undergo partial dehydration and penetrate through the first water layer next to the graphene electrode surfaces under charging. As such, the electrical potential distribution through the EDL strongly depends on the ion type. Interestingly, we further reveal that the water can play a critical role in determining the capacitance value. The change of dielectric constant of water in different electrolytes largely cancels out the variance in electric potential drop across the EDL of different ion type. Our simulation sheds new lights on how the interplay between solvent molecules and EDL structure cooperatively contributes to capacitance, which agrees with our experimental results well.