Detecting abusive language in social media conversations poses significant challenges, as identifying abusiveness often depends on the conversational context, characterized by the content and topology of preceding comments. Traditional Abusive Language Detection (ALD) models often overlook this context, which can lead to unreliable performance metrics. Recent Natural Language Processing (NLP) methods that integrate conversational context often depend on limited and simplified representations, and report inconsistent results. In this paper, we propose a novel approach that utilize graph neural networks (GNNs) to model social media conversations as graphs, where nodes represent comments, and edges capture reply structures. We systematically investigate various graph representations and context windows to identify the optimal configuration for ALD. Our GNN model outperform both context-agnostic baselines and linear context-aware methods, achieving significant improvements in F1 scores. These findings demonstrate the critical role of structured conversational context and establish GNNs as a robust framework for advancing context-aware abusive language detection.