A new approach to the characterization of network connectivity under transmission rate and secrecy constraints is proposed, based on a rate-secrecy graph model. The proposed model is based on an information theoretic framework, and rate-distortion requirements are used to characterize the level of secrecy for individual links in the network. Rate-secrecy-connectivity tradeoffs are illustrated and it is shown that by relaxing the secrecy constraint, an acceptable secrecy level can be achieved while significantly improving network connectivity and transmission rate efficiency for the wireless nodes.