In the complex landscape of hematologic samples such as peripheral blood or bone marrow, cell classification, delineating diverse populations into a hierarchical structure, presents profound challenges. This study presents LeukoGraph, a recently developed framework designed explicitly for this purpose employing graph attention networks (GATs) to navigate hierarchical classification (HC) complexities. Notably, LeukoGraph stands as a pioneering effort, marking the application of graph neural networks (GNNs) for hierarchical inference on graphs, accommodating up to one million nodes and millions of edges, all derived from flow cytometry data. LeukoGraph intricately addresses a classification paradigm where for example four different cell populations undergo flat categorization, while a fifth diverges into two distinct child branches, exemplifying the nuanced hierarchical structure inherent in complex datasets. The technique is more general than this example. A hallmark achievement of LeukoGraph is its F-score of 98%, significantly outclassing prevailing state-of-the-art methodologies. Crucially, LeukoGraph's prowess extends beyond theoretical innovation, showcasing remarkable precision in predicting both flat and hierarchical cell types across flow cytometry datasets from 30 distinct patients. This precision is further underscored by LeukoGraph's ability to maintain a correct label ratio, despite the inherent challenges posed by hierarchical classifications.