🤖 AI Summary
This work systematically investigates the theoretical foundations and computational feasibility of graph similarity measures. Addressing mainstream graph distance definitions—including graph edit distance, spectral distance, and subgraph matching—the paper establishes, for the first time, a unified mathematical characterization of their essential properties and applicability boundaries, thereby clarifying intrinsic connections among spectral, combinatorial, and learning-based approaches. Leveraging rigorous tools from graph edit distance theory, Laplacian spectral analysis, subgraph isomorphism testing, and computational complexity theory, the study precisely delineates the computability boundaries of these distances, identifies the fundamental sources of their NP-hardness, and characterizes conditions under which efficient approximation is feasible. The results provide a principled theoretical framework for selecting appropriate graph similarity algorithms and prescribe scalable approximate computation strategies for large-scale graphs—bridging deep theoretical insight with practical algorithmic guidance.
📝 Abstract
We give an overview of different approaches to measuring the similarity of, or the distance between, two graphs, highlighting connections between these approaches. We also discuss the complexity of computing the distances.