It is generally accepted that building software out of loosely coupled components, such as in service-oriented systems or mobile networks, yields applications that are more robust against changes and failure of single components than monolithic systems. In order to accommodate for changes in the environment or in the requirements, and anticipate to a component failure, applications are often dynamically adapted by means of a reconfiguration. In this paper, we target the visual channel-based coordination language Reo and introduce a combined structural and behavioral model for graph-based component connectors in Reo. Exploiting concepts from category theory, we model reconfigurations of connectors as transformations of the underlying connector graphs. We show that our connector model has a compositional semantics and lift structural reconfigurations to the semantical level. As a concrete application of our framework, we introduce a notion of behavior-preserving reconfiguration for Reo and provide a sufficient condition to ensure behavior-preservation statically.