Graph transformation systems (GTS) and constraint handling rules (CHR) are non-deterministic rule-based state transition systems. CHR is well-known for its powerful confluence and program equivalence analyses, for which we provide the basis in this work to apply them to GTS. We give a sound and complete embedding of GTS in CHR, investigate confluence of an embedded GTS, and provide a program equivalence analysis for GTS via the embedding. The results confirm the suitability of CHR-based program analyses for other formalisms embedded in CHR.