This paper focuses on the integration of passive and active network monitoring techniques in Grid systems. We propose a number of performance metrics for assessing the quality of the connectivity, and describe the required measurement methods for obtaining these metrics. Furthermore, the issue of efficiently representing and publishing the measured values is considered. We show that it is important to have both active and passive monitoring strategies applied to Grid systems; and when we do have both strategies it is necessary to have an a priory hybrid design. Finally we depict the tradeoffs introduced by this approach and the description of the components for a domain oriented monitoring infrastructure that supports both passive and active monitoring tools in Grid systems.