Flight delays due to holding maneuvers are a critical and costly phenomenon in aviation, driven by the need to manage air traffic congestion and ensure safety. Holding maneuvers occur when aircraft are instructed to circle in designated airspace, often due to factors such as airport congestion, adverse weather, or air traffic control restrictions. This study models the prediction of flight delays due to holding maneuvers as a graph problem, leveraging advanced Graph Machine Learning (Graph ML) techniques to capture complex interdependencies in air traffic networks. Holding maneuvers, while crucial for safety, cause increased fuel usage, emissions, and passenger dissatisfaction, making accurate prediction essential for operational efficiency. Traditional machine learning models, typically using tabular data, often overlook spatial-temporal relations within air traffic data. To address this, we model the problem of predicting holding as edge feature prediction in a directed (multi)graph where we apply both CatBoost, enriched with graph features capturing network centrality and connectivity, and Graph Attention Networks (GATs), which excel in relational data contexts. Our results indicate that CatBoost outperforms GAT in this imbalanced dataset, effectively predicting holding events and offering interpretability through graph-based feature importance. Additionally, we discuss the model's potential operational impact through a web-based tool that allows users to simulate real-time delay predictions. This research underscores the viability of graph-based approaches for predictive analysis in aviation, with implications for enhancing fuel efficiency, reducing delays, and improving passenger experience.