Brain functional networks have been traditionally studied considering only interactions between pairs of regions, neglecting the richer information encoded in higher orders of interactions. In consequence, most of the connectivity studies in neurodegeneration and dementia use standard pairwise metrics. Here, we developed a genuine high-order functional connectivity (HOFC) approach that captures interactions between 3 or more regions across spatiotemporal scales, delivering a more biologically plausible characterization of the pathophysiology of neurodegeneration. We applied HOFC to multimodal (electroencephalography [EEG], and functional magnetic resonance imaging [fMRI]) data from patients diagnosed with behavioral variant of frontotemporal dementia (bvFTD), Alzheimer's disease (AD), and healthy controls. HOFC revealed large effect sizes, which, in comparison to standard pairwise metrics, provided a more accurate and parsimonious characterization of neurodegeneration. The multimodal characterization of neurodegeneration revealed hypo and hyperconnectivity on medium to large-scale brain networks, with a larger contribution of the former. Regions as the amygdala, the insula, and frontal gyrus were associated with both effects, suggesting potential compensatory processes in hub regions. fMRI revealed hypoconnectivity in AD between regions of the default mode, salience, visual, and auditory networks, while in bvFTD between regions of the default mode, salience, and somatomotor networks. EEG revealed hypoconnectivity in the γ band between frontal, limbic, and sensory regions in AD, and in the δ band between frontal, temporal, parietal and posterior areas in bvFTD, suggesting additional pathophysiological processes that fMRI alone can not capture. Classification accuracy was comparable with standard biomarkers and robust against confounders such as sample size, age, education, and motor artifacts (from fMRI and EEG). We conclude that high-order interactions provide a detailed, EEG- and fMRI compatible, biologically plausible, and psychopathological-specific characterization of different neurodegenerative conditions.