In this paper we propose an extension of the rho-calculus, called rhoG-calculus, handling structures with cycles and sharing rather than simple terms. This is obtained by using recursion constraints in addition to the standard rho-calculus matching constraints, which leads to a term-graph representation in an equational style. As for the rho-calculus, 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.