Dementia affects over 55 million people worldwide, projected to reach 139 million by 2050, with Alzheimer's disease (AD) accounting for 60-70% of cases. AD is associated with disruptions in metabolic brain connectivity. Detecting these disruptions early is crucial for AD management. FDG-PET is a useful tool for identifying such impairments. However, most studies rely on group-level analyses or thresholding, potentially masking individual differences and overlooking weaker yet biologically critical brain connections. Moreover, AD prediction largely focuses on univariate rather than multivariate outcomes. To address this, we introduce explainable graph-theoretical machine learning (XGML), a framework for constructing individual metabolic brain graphs and identifying subgraphs most predictive of multivariate disease-related outcomes. Using Alzheimer's Disease Neuroimaging Initiative (ADNI) FDG-PET data, we compared six graph representations against three non-graph baselines, each with six machine learning models using repeated stratified 3-fold cross-validation (10 repeats). The best configuration combined kernel density estimation with Hellinger distance and random forest. Across eight cognitive scores, it reached an overall Fisher-z-averaged Pearson correlation of r=0.595, with strongest performance for ADAS13 (r=0.67), ADAS11 (r=0.65), and ADASQ4 (r=0.62). We identified key edges that were jointly but differentially predictive across outcomes, suggesting their potential as network biomarkers of cognitive decline. Preliminary external feasibility validation on an OASIS3 cohort yielded weak predictive performance for CDRSB (r=0.26) and MMSE (r=0.18), likely reflecting cohort, protocol, and diagnostic differences. Overall, our results suggest the promise of graph-theoretical machine learning for biomarker discovery, disease prediction, and understanding the neural mechanisms underlying AD.

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