  For any unital commutative ring $R$ and for any graph $E$, we identify the
commutative core of the Leavitt path algebra of $E$ with coefficients in $R$,
which is a maximal commutative subalgebra of the Leavitt path algebra.
Furthermore, we are able to characterize injectivity of representations which
gives a generalization of the Cuntz-Krieger uniqueness theorem.
