This paper presents the Advanced Syntactic-Graph Convolutional Model (ASGCM), a pioneering approach in Aspect-Based Sentiment Analysis (ABSA) that integrates syntactic dependency features within a graph convolution framework. ASGCM stands out for its novel use of dependency edge encoding and tag-based graph convolutions, providing a fine-grained analysis of sentiments associated with specific aspects in text. This model meticulously captures the intricacies of syntactic structures, thereby offering enhanced precision in sentiment analysis. Notably, ASGCM incorporates a dual-layer graph convolution system: one layer processes syntactic dependencies (edges), while the other interprets semantic roles (tags), ensuring a comprehensive understanding of both structural and contextual elements in text. We rigorously tested ASGCM on multiple datasets, including both English and Chinese languages, and our findings reveal a significant improvement in sentiment classification accuracy compared to existing models. The versatility of ASGCM makes it a robust tool for diverse linguistic environments, setting a new standard for ABSA methodologies.