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The collectivity of the electronic motion in graphene nanostructures is studied by time-dependent density functional theory (TDDFT). Compared with the plasmon in the homogeneous graphene, the plasmon in the graphene nanostructure has some different properties due to the effect of the size and the all dimensional confinement. In lower-energy resonance zone, spectral band is greatly broadening, even extending to the near-infrared spectral area, and the photoabsorption strength line splits. The absorption spectrum also depends on the edge configuration of the graphene nanostructure. The armchair-edge and the zigzag-edge play different roles in the absorption spectrum. Moreover, our results also demonstrate that most low-energy resonances are localized in the boundary region. [ABSTRACT FROM AUTHOR]