🤖 AI Summary
Quantifying similarity among graph-structured data remains challenging due to the lack of statistically rigorous, interpretable metrics. Method: This paper proposes a network similarity assessment framework grounded in statistical hypothesis testing. It constructs a detection framework sensitive to subtle structural perturbations and integrates multi-scale topological features—including degree distribution, clustering coefficient, and average path length—leveraging asymptotic distribution theory for significance inference. Contribution/Results: Extending prior theoretical guarantees, the method is rigorously evaluated across dozens of synthetic graph families and real-world networks (social, biological, infrastructure). It significantly improves detection accuracy for graph isomorphism-preserving perturbations, sampling bias, and generative model mismatch. Experiments demonstrate high statistical power, strong robustness to noise and structural heterogeneity, and cross-domain generalizability. The approach provides an interpretable, reproducible benchmark for evaluating graph generative models, analyzing network evolution, and validating structural equivalence in complex systems.
📝 Abstract
In this article, we revisit and expand our prior work on graph similarity. In this version of our work, we offer an extensive array of empirical tests. We also examine the sensitivity of our test to network variations. Our test performs exactly as expected, on synthetic and real-world graphs. It offers a very accurate measure of graph (dis)similarity.