We propose a novel approach for the reconstruction of functional networks representing brain dynamics based on the idea that the co-participation of two brain regions in a common cognitive task should result in a drop in their identifiability, or in the uniqueness of their dynamics. This identifiability is estimated through the score obtained by Deep Learning models in supervised classification tasks; and therefore requires no a priori assumptions about the nature of such co-participation. The method is tested on EEG recordings obtained from Alzheimer‘s and Parkinson‘s Disease patients, and matched healthy volunteers, for eyes-open and eyes-closed resting state conditions; and the resulting functional networks are analysed through standard topological metrics. Both groups of patients are characterised by a reduction in the identifiability of the corresponding EEG signals, and by differences in the patterns that support such identifiability. Resulting functional networks are similar, but not identical to those reconstructed by using a correlation metric. Differences between control subjects and patients can be observed in network metrics like the clustering coefficient and the assortativity, in different frequency bands. Differences are also observed between eyes-open and closed conditions, especially for Parkinson‘s Disease patients.