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We experimentally investigated the vector multi-soliton operation and vector soliton interaction in an erbium doped fiber laser passively mode locked by atomic layer graphene. It is found that the vector multi-soliton operation exhibited several characteristic modes. These are the random static distribution of vector solitons, stable bunches of vector solitons, restless oscillations of vector solitons, rain of vector solitons, and emission of a so-called “giant vector soliton”. The formation mechanisms of the operation modes were also experimentally investigated.