Conventional brain connectivity analysis is typically based on the assessment of interregional correlations. Given that correlation coefficients are derived from both covariance and variance, group differences in covariance may be obscured by differences in the variance terms. To facilitate a comprehensive assessment of connectivity, we propose a unified statistical framework that interrogates the individual terms of the correlation coefficient. We have evaluated the utility of this method for metabolic connectivity analysis using [18F]2-fluoro-2-deoxyglucose (FDG) positron emission tomography (PET) data from the Alzheimer's Disease Neuroimaging Initiative (ADNI) study. As an illustrative example of the utility of this approach, we examined metabolic connectivity in angular gyrus and precuneus seed regions of mild cognitive impairment (MCI) subjects with low and high β-amyloid burdens. This new multivariate method allowed us to identify alterations in the metabolic connectome, which would not have been detected using classic seed-based correlation analysis. Ultimately, this novel approach should be extensible to brain network analysis and broadly applicable to other imaging modalities, such as functional magnetic resonance imaging (MRI).