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In this paper, the possibility of detecting topological variations by observing output trajectories from networked linear time-invariant systems is investigated, where the network topology can be general, but the nodes have identical higher-dimensional dynamics. A necessary and sufficient condition on the discernibility of topological variations is derived, in terms of the eigenspaces of the original and the modified network configuarations. By taking the specific network structures into consideration, some lower-dimensional conditions are derived, which reveal how the network topologies, sensor locations, node-system dynamics and output, as well as inner interactions altogether affect the discernibility. Furthermore, the output discernibility of topological changes for networked multi-agent systems is revisited, showing that some criterion reported in the literature does not hold. Consequently, a modified necessary and sufficient condition is established. The effectiveness of the results is demonstrated through several examples.