Here we presented a single electroencephalographic (EEG) marker for a neurophysiological assessment of Alzheimer’s disease (AD) patients already diagnosed by current guidelines. The ability of the EEG marker to classify 127 AD individuals and 121 matched cognitively intact normal elderly (Nold) individuals was tested. Furthermore, its relationship to AD patients’ cognitive status and structural brain integrity was examined. Low-resolution brain electromagnetic tomography (LORETA) freeware estimated cortical sources of resting state eyes-closed EEG rhythms. The EEG marker was defined as the ratio between the activity of parieto-occipital cortical sources of delta (2–4 Hz) and low-frequency alpha (8–10.5 Hz) rhythms. Results showed 77.2% of sensitivity in the recognition of the AD individuals; 65% of specificity in the recognition of the Nold individuals; and 0.75 of area under the receiver-operating characteristic curve. Compared to the AD subgroup with the EEG maker within one standard deviation of the Nold mean (EEG-), the AD subgroup with EEG+ showed lower global cognitive status, as revealed by Mini-Mental State Evaluation score, and more abnormal values of white-matter and cerebrospinal fluid normalized volumes, as revealed by structural magnetic resonance imaging. We posit that cognitive and functional status being equal, AD patients with EEG+ should receive special clinical attention due to a neurophysiological “frailty”. EEG+ label can be also used in clinical trials (i) to form homogeneous groups of AD patients diagnosed by current guidelines and (ii) as end-point to evaluate intervention effects.