Optimized geometries and electronic structures of two different hexagonal grapheme nanosheets (HGNSs), with armchair (n-A-HGNS, n = 3-11) and zigzag (n-Z-HGNS, n = 1-8) edges have been calculated by using the GGA/PBE method implemented in the SIESTA package, with the DZP basis set, where n represents the number of peripheral rings. The computed HOMO-LUMO energy gap (Eg = ELUMO - EHOMO) decreases for fully H-terminated A- and Z-HGNSs with increasing n, i.e., with increasing nanosheet size and pπ-orbitals being widely delocalized over the sheet surface. The full terminations, calculated with various functional groups, including the electron-withdrawing (F-, Cl-, and CN-) and -donating (OH-, and SH-) substitutions, were addressed. Significant lowering of EHOMO and ELUMO was obtained for CN-terminated HGNS as compared to those for H-terminated ones due to the mesomeric effect. The calculated Eg value decreases with increasing n for all terminations, whereby for the SH-termination in HGNS, the termination effect becomes less significant with increasing n. Further, the calculation results for stabilities of HGNS oxides support the tendency toward the oxidative reactivity at the edge site of the sheet, which shows most pronounced C-C bond length alternation, by chemical modification. Physical properties of HGNSs with various numbers of the core-defects, which can be obtained by strong oxidation, were also investigated. Their structures can change drastically from planar to saddle-like shapes. These conformations could be used as stationary phases with controlled interaction in the separation methods such as HPLC and the other chemical analysis techniques.