In order to cope with the exponential time complexity of graph edit distance, several polynomial-time approximation algorithms have been proposed in recent years. The Hausdorff edit distance is a quadratic-time matching procedure for labeled graphs which reduces the edit distance to a correspondence problem between local substructures. In its original formulation, nodes and their adjacent edges have been considered as local substructures. In this paper, we integrate a more general structural node context into the matching procedure based on hierarchical subgraphs. In an experimental evaluation on diverse graph data sets, we demonstrate that the proposed generalization of Hausdorff edit distance can significantly improve the accuracy of graph classification while maintaining low computational complexity.