Simple modules of Leavitt path algebras when the coefficients are in a commutative ring

We use subcategories of the module category of a Leavitt path algebra of a finite digraph Gamma with pairwise disjoint cycles when the coefficients are from a unital commutative ring k, to classify all simple modules in terms of the sinks and the cycles of Gamma (reducing the question to cycles without exit in a subgraph) and the maximal ideals of k or k[x,x(-1)]. Our classification becomes more explicit and straightforward if the coefficient ring is a field.