Measuring graph similarity is a key issue in many applications. We propose a new constraint-based modeling language for defining graph similarity measures by means of constraints. It covers measures based on univalent matchings, such that each node is matched with at most one node, as well as multivalent matchings, such that a node may be matched with a set of nodes. This language is designed on top of Comet, a programming language supporting both Constraint Programming (CP) and Constraint-Based Local Search (CBLS). Starting from the constraint-based description of the measure, we automatically generate a Comet program for computing the measure. Depending on the measure characteristics, this program either uses CP ---which is better suited for computing exact measures such as (sub)graph isomorphism--- or CBLS ---which is better suited for computing error-tolerant measures such as graph edit distances. First experimental results show the feasibility of our approach.