Leveraging recent advances in graph neural networks, our study introduces an application of graph convolutional networks (GCNs) within a correlation-based population graph, aiming to enhance Alzheimer’s disease (AD) prognosis and illuminate the intricacies of AD progression. This methodological approach leverages the inherent structure and correlations in demographic and neuroimaging data to predict amyloid-beta (Aβ) positivity. To validate our approach, we conducted extensive performance comparisons with conventional machine learning models and a GCN model with randomly assigned edges. The results consistently highlighted the superior performance of the correlation-based GCN model across different sample groups in the Alzheimer’s Disease Neuroimaging Initiative (ADNI) dataset, suggesting the importance of accurately reflecting the correlation structure in population graphs for effective pattern recognition and accurate prediction. Furthermore, our exploration of the model’s decision-making process using GNNExplainer identified unique sets of biomarkers indicative of Aβpositivity in different groups, shedding light on the heterogeneity of AD progression. This study underscores the potential of our proposed approach for more nuanced AD prognoses, potentially informing more personalized and precise therapeutic strategies. Future research can extend these findings by integrating diverse data sources, employing longitudinal data, and refining the interpretability of the model, which potentially has broad applicability to other complex diseases.