Indexing Method for Hierarchical Graphs based on Relation among Interlacing Sequences of Eigenvalues

Abstract

We propose an indexing method for hierarchical graphs using their eigenvalues in order to detect those that are substructures or superstructures of a hierarchical graph given as a query efficiently. The index construction and the query processing are based on a relation among three interlacing sequences of eigenvalues of hierarchical graphs. We also propose a matrix representation for a hierarchical graph. Hierarchical graphs are decomposed to improve the filtering effect of the index and reduce the computational cost of both the index construction and the query processing. We evaluate the effectiveness of the proposed method by experiments.