In this paper, controllability properties of networks of diffusively coupled linear systems are considered through the controllability Gramian. For a class of passive linear systems, it is shown that the controllability Gramian can be decomposed into two parts. The first part is related to the dynamics of the individual systems whereas the second part is dependent only on the interconnection topology, allowing for a clear interpretation and efficient computation of controllability properties for a class of networked systems. Moreover, a relation between symmetries in the interconnection topology and controllability is given. The results are illustrated by an example.