The photonic graphene in atoms not only has the typical photonic band structures but also exhibits controllable optical properties that are difficult to achieve in the natural graphene. Here, the evolution process of discrete diffraction patterns of a photonic graphene, which is constructed through a three-beam interference, is demonstrated experimentally in a 5S1/2 - 5P3/2 - 5D5/2 85Rb atomic vapor. The input probe beam experiences a periodic refractive index modulation when traveling through the atomic vapor, and the evolution of output patterns with honeycomb, hybrid-hexagonal, and hexagonal geometric profiles is obtained by controlling the experimental parameters of two-photon detuning and the power of the coupling field. Moreover, the Talbot images of such three kinds of periodic structure patterns at different propagating planes are observed experimentally. This work provides an ideal platform to investigate manipulation the propagation of light in artificial photonic lattices with tunable periodically varying refractive index.