Towards Subgraph Isomorphism Counting with Graph Kernels
This work addresses a #P-complete problem in graph theory with potential applications in domains like bioinformatics and social network analysis, but it appears incremental as it builds on existing graph kernel methods.
The paper tackles the computationally hard problem of subgraph isomorphism counting by exploring graph kernels, which are enhanced with neighborhood information to approximate solutions more effectively.
Subgraph isomorphism counting is known as #P-complete and requires exponential time to find the accurate solution. Utilizing representation learning has been shown as a promising direction to represent substructures and approximate the solution. Graph kernels that implicitly capture the correlations among substructures in diverse graphs have exhibited great discriminative power in graph classification, so we pioneeringly investigate their potential in counting subgraph isomorphisms and further explore the augmentation of kernel capability through various variants, including polynomial and Gaussian kernels. Through comprehensive analysis, we enhance the graph kernels by incorporating neighborhood information. Finally, we present the results of extensive experiments to demonstrate the effectiveness of the enhanced graph kernels and discuss promising directions for future research.