We study, in this paper, the physical properties of water confined between two parallel graphene plates with different slit widths to understand the effects of confinement on the water structure and how bulk properties are reached as the water layer thickens. It was found that the microscopic structures of the interfacial liquid layer close to graphene vary with the slit width. Water tends to locate at the center of the six-membered ring of graphene planes to form triangular patterns, as found by others. The narrower the slit width is, the more pronounced this pattern is, except for the slit width of 9.5 Å, for which a well-defined two-layer structure of water forms. On the other hand, squared structures can be clearly seen in single snapshots at small (6.5 Å and 7.5 Å) but not large slit widths. Even at small slit widths, the square-like geometry is observed only when an average is taken for a short trajectory, and averaging over a long time yields a triangular pattern dictated by the graphene geometry. We estimate the length of time needed to observe two patterns, respectively. We also used the two-phase thermodynamic model to study the variation of entropy of confined water and found that at 8.5 Å, the entropy of confined water is larger than that of bulk water. The rotational entropy of confined water is higher than that of bulk water for all slit widths due to the reduction of the hydrogen bond in the confined space.