The aim of this research was to study the changes that Alzheimer's disease (AD) elicits in the organization of brain networks. For this task, the electroencephalographic (EEG) activity from 32 AD patients and 25 healthy controls was analyzed. In a first step, a disequilibrium measure, the Euclidean distance (ED), was used to estimate the similarity between the spectral content of each pair of electrodes. In a second step, the similarity matrices were used to generate the corresponding graphs, from which two parameters were computed to characterize the network structure: the mean clustering coefficient and the mean path length. Results revealed significant changes (p<0.05) in ED values, as well as in the mean clustering coefficient and the mean path length, though they depend on the specific frequency band. Our findings suggest that AD is accompanied by a significant frequency-dependent alteration of brain network organization.