Alzheimer’s Disease (AD) is a neurological disorder characterized by a progressive deterioration of brain functions that affects, above all, older adults. It can be difficult to make an early diagnosis because its first symptoms are often associated with normal aging. Electroencephalography (EEG) can be used for evaluating the loss of brain functional connectivity in AD patients. The purpose of this paper is to study the brain network parameters through the estimation of Lagged Linear Connectivity (LLC), computed by eLORETA software, applied to High-Density EEG (HD-EEG) for 84 regions of interest (ROIs). The analysis involved three groups of subjects: 10 controls (CNT), 21 Mild Cognitive Impairment patients (MCI) and 9 AD patients. In particular, the purpose is to compare the results obtained using a 256-channel EEG, the corresponding 10–10 system 64-channel EEG and the corresponding 10–20 system 18-channel EEG, both of which are extracted from the 256-electrode configuration. The computation of the Characteristic Path Length, the Clustering Coefficient, and the Connection Density from HD-EEG configuration reveals a weakening of small-world properties of MCI and AD patients in comparison to healthy subjects. On the contrary, the variation of the network parameters was not detected correctly when we employed the standard 10–20 configuration. Only the results from HD-EEG are consistent with the expected behavior of the AD brain network.