Alzheimer's Disease (AD) is a neurodegenerative disorder that causes a loss of connections between neurons. The goal of the present work was to construct a complex network model of the brain-electrical activity using high-density EEG (HD-EEG) recordings and to compare the network organization in AD, Mild Cognitive Impaired (MCI) and healthy control (CNT) subjects. The HD-EEG of 16 AD, 16 MCI and 12 CNT were recorded during an eye-closed resting state. The Permutation Disalignment Index (PDI) was used to describe the dissimilarity between EEG signals and to construct the connection matrices of the network model. The three groups were found to have significantly different ( $p\lt0.001$ ) Characteristic Path Length (Lambda), average Clustering Coefficient (CC) and Global Efficiency (GE). This is the first time that HD-EEG signals of AD, MCI and CNT have been compared and that PDI has been used to discriminate between the three groups. Considered the large amount of data originating from the HD-EEG acquisition, compared to standard EEG, the aim of the present work was also to assess that compression did not alter the results of the complex network analysis. Compressive sensing was adopted to compress and reconstruct the HD-EEG signals with minimal information loss, achieving an average Structural SIMilarity index (SSIM) of 0.954 (AD), 0.957 (MCI) and 0.959 (CNT). When applied to the reconstructed HD-EEG, the complex network analysis provided a substantially unaltered performance, compared to the analysis of the original signals. Indeed, Lambda, CC, GE and of the three groups were still significantly different ( $p\lt0.001$ ).

In this paper, a novel electroencephalographic (EEG)-based method is introduced for the quantification of brain-electrical connectivity changes over a longitudinal evaluation of mild cognitive impaired (MCI) subjects. In the proposed method, a dissimilarity matrix is constructed by estimating the coupling strength between every pair of EEG signals, Hierarchical clustering is then applied to group the related electrodes according to the dissimilarity estimated on pairs of EEG recordings. Subsequently, the connectivity density of the electrodes network is calculated. The technique was tested over two different coupling strength descriptors: wavelet coherence (WC) and permutation Jaccard distance (PJD), a novel metric of coupling strength between time series introduced in this paper. Twenty-five MCI patients were enrolled within a follow-up program that consisted of two successive evaluations, at time T0 and at time T1, three months later. At T1, four subjects were diagnosed to have converted to Alzheimer's Disease (AD). When applying the PJD-based method, the converted patients exhibited a significantly increased PJD (p < 0.05), i.e., a reduced overall coupling strength, specifically in delta and θ bands and in the overall range (0.5-32 Hz). In addition, in contrast to stable MCI patients, converted patients exhibited a network density reduction in every subband (delta, θ, alpha, and beta). When WC was used as coupling strength descriptor, the method resulted in a less sensitive and specific outcome. The proposed method, mixing nonlinear analysis to a machine learning approach, appears to provide an objective evaluation of the connectivity density modifications associated to the MCI-AD conversion, just processing noninvasive EEG signals.