The entanglement properties of a multiparty pure state are invariant under local unitary transformations. The stabilizer dimension of a multiparty pure state characterizes how many types of such local unitary transformations existing for the state. W
e find that the stabilizer dimension of an $n$-qubit ($nge 2$) graph state is associated with three specific configurations in its graph. We further show that the stabilizer dimension of an $n$-qubit ($nge 3$) graph state is equal to the degree of irreducible two-qubit correlations in the state.
