The functional equivalence between mental images and perception or motion has been proposed on the basis of neuroimaging evidence of large spatially overlapping activations between real and imagined sensori-motor conditions. However, similar local activation patterns do not imply the same mesoscopic integration of brain regions active during imagery and perception or action. Here we present the first EEG evidence of topological equivalence between functional network organization at intermediate and global scales during tasks. We show that the degree of functional equivalence varies in the population and is associated with different magnitudes in the restructuring of the functional connectivity between imagery and real tasks. In particular, changes observed during imagery with respect to basal conditions account for the cognitive effort experienced during imagery, and subjects characterized by stronger functional equivalence exhibit smaller topological deviations in the imagination tasks performed after real tasks, thus showing learning effects. Altogether, our findings point to different sensori-cognitive information processing in the subjects showing different functional equivalence. We anticipate our results to be a starting point for a novel dynamical description of functional equivalence, which will be relevant for socio-cognitive theories of embodiment and cognitive formulations of how different selves emerge from neurophysiological assets.