The application of Self-Organizing Map (SOM) to hierarchical data remains an open issue, because such data lack inherent quantitative information. Past studies have suggested binary encoding and Generalizing SOM as techniques that transform hierarchical data into numerical attributes. Based on graph theory, this paper puts forward a novel approach that processes hierarchical data into a numerical representation for SOM-based clustering. The paper validates the proposed graph-theoretical approach via complexity theory and experiments on real-life data. The results suggest that the graph-theoretical approach has lower algorithmic complexity than Generalizing SOM, and can yield SOM having significantly higher cluster validity than binary encoding does. Thus, the graph-theoretical approach can form a data-preprocessing step that extends SOM to the domain of hierarchical data.