Alzheimer's disease (AD) is a progressive neurological disorder characterized by the gradual deterioration of cognitive functions, leading to dementia and significantly impacting the quality of life for millions of people worldwide. Early and accurate diagnosis is crucial for the effective management and treatment of this debilitating condition. This study introduces a novel framework based on Spectral Graph Convolutional Neural Networks (SGCNN) for diagnosing AD and categorizing multiple diseases through the analysis of functional changes in brain structures captured via magnetic resonance imaging (MRI). To assess the effectiveness of our approach, we systematically analyze structural modifications to the SGCNN model through comprehensive ablation studies. The performance of various Convolutional Neural Networks (CNNs) is also evaluated, including SGCNN variants, Base CNN, Lean CNN, and Deep CNN. We begin with the original SGCNN model, which serves as our baseline and achieves a commendable classification accuracy of 93%. In our investigation, we perform two distinct ablation studies on the SGCNN model to examine how specific structural changes impact its performance. The results reveal that Ablation Model 1 significantly enhances accuracy, achieving an impressive 95%, while Ablation Model 2 maintains the baseline accuracy of 93%. Additionally, the Base CNN model demonstrates strong performance with a classification accuracy of 93%, whereas both the Lean CNN and Deep CNN models achieve 94% accuracy, indicating their competitive capabilities. To validate the models' effectiveness, we utilize multiple evaluation metrics, including accuracy, precision, recall, and F1-score, ensuring a thorough assessment of their performance. Our findings underscore that Ablation Model 1 (SGCNN Model 1) delivers the highest predictive accuracy among the tested models, highlighting its potential as a robust approach for Alzheimer's image classification. Ultimately, this research aims to facilitate early diagnosis and treatment of AD, contributing to improved patient outcomes and advancing the field of neurodegenerative disease diagnosis.