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Silicon-based electro-optic modulators are the key devices in integrated optoelectronics. Integration of the graphene layer and the photonic crystal (PC) cavity is a promising way of achieving compact modulators with high efficiency. In this paper, a high-quality (Q) acceptor-type PC nanocavity is employed to integrate with a single-layer graphene for realizing strong modulation. Through tuning the chemical potential of graphene, a large wavelength shift of 2.62 nm and a Q factor modulation of larger than 5 are achieved. A modulation depth (12.8 dB) of the reflection spectrum is also obtained. Moreover, the optimized PC nanocavity has a large free spectral range of 131.59 nm, which can effectively enhance the flexibility of the modulator. It shows that the proposed graphene-based PC nanocavity is a potential candidate for compact, high-contrast, and low-power absorptive modulators in integrated silicon chips. [ABSTRACT FROM AUTHOR]