The graph rewriting calculus is an extension of the $\rho$-calculus, handling graph like structures rather than simple terms. The calculus over terms is naturally generalized by using unification constraints in addition to the standard rho-calculus matching constraints. The transformations are performed by explicit application of rewrite rules as first class entities. The possibility of expressing sharing and cycles allows one to represent and compute over regular infinite entities. We propose in this paper a reduction strategy for the graph rewriting calculus which aims at maintaining the sharing information as long as possible in the terms. The corresponding reduction relation is shown to be confluent and complete with regards to the small-step semantics of the graph rewriting calculus.