A Study of Laplacian Spectra of Graph for Subgraph Queries

The spectrum of graph has been widely used in graph mining to extract graph topological information. It has also been employed as a characteristic of graph to check the sub graph isomorphism testing since it is an invariant of a graph. However, the spectrum cannot be directly applied to a graph and its sub graph, which is a bottleneck for sub graph isomorphism testing. In this paper, we study the Laplacian spectra between a graph and its sub graph, and propose a method by straightforward adoption of them for sub graph queries. In our proposed method, we first encode every vertex and graph by extracting their Laplacian spectra, and generate a novel two-step filtering conditions. Then, we follow the filtering-and verification framework to conduct sub graph queries. Extensive experiments show that, compared with existing counterpart method, as a graph feature, Laplacian spectra can be used to efficiently improves the efficiency of sub graph queries and thus indicate that it have considerable potential.