We study the data transformation capabilities associated with schemas that are presented by directed multi-graphs and path equations. Unlike most approaches which treat graph-based schemas as abbreviations for relational schemas, we treat graph-based schemas as categories. A schema S is a finitely-presented category, and the collection of all S-instances forms a category, S–Inst. A functor F between schemas S and T, which can be generated from a visual mapping between graphs, induces three adjoint data migration functors, ΣF : S–Inst → T–Inst, ΠF : S–Inst → T–Inst, and ∆F : T–Inst → S–Inst. We present an algebraic query language FQL based on these functors, prove that FQL is closed under composition, prove that FQL can be implemented with the select-project-product-union relational algebra (SPCU) extended with a key-generation operation, and prove that SPCU can be implemented with FQL.