Graph neural networks (GNNs) have emerged as powerful tools for analyzing graph-structured data with applications in social networks, bioinformatics, and recommender systems. However, existing GNNs struggle with (1) rigid edge weighting (e.g., GCN’s fixed normalization), (2) over-smoothing in deep layers, and (3) quadratic attention costs (e.g., GAT). MGCN introduces: (1) adaptive edge weighting to dynamically adjust neighbor influence, (2) residual connections to combat over-smoothing, and (3) a scalable attention mechanism. It also introduces a standardized evaluation framework that incorporates adaptive preprocessing techniques such as feature normalization, edge weighting, and graph augmentation. The proposed model demonstrated superior performance when compared to eight state-of-the-art GNN models such as GraphSAGE, GAT, Graph Transformer, GINConv, GCN, GraphCL, AGCN, and MGCN, across three widely used benchmark datasets: Cora, CiteSeer, and PubMed. All evaluation metrics–including Accuracy, Hit Ratio, Precision, Recall, and F1 Score–are reported as the mean ± standard deviation over 10 independent runs. The experimental results consistently demonstrate the superiority of the proposed MGCN model with approximately 2% improvement on above datasets.