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About this paper
Gecia Bravo-Hermsdorff, Lee M. Gunderson, Pierre-André Maugis, Carey E. Priebe
The paper compares graph samples using graph cumulants, which measure connected subgraph densities after accounting for contributions from smaller substructures. It matches a moments-based squared Mahalanobis test, using the same graphon assumptions, subgraph inputs, and computational complexity. In tested three-edge settings, cumulants support one graph per sample, whereas moments require at least four; broader claims are not established.
Key insights
- Graph cumulants serve as a more natural and statistically advantageous set of coordinates for characterizing network structure, as they quantify substructure propensities in a way that is less correlated with lower-order effects.
- The distribution of the cumulant-based test statistic under the null hypothesis closely approximates a chi-squared distribution, even with small sample sizes, leading to improved control over false positive rates.
- The cumulant-based approach enables robust statistical inference about a graph distribution even from a single observed graph, a capability generally unavailable with graph moment-based tests, by effectively leveraging internal data multiplicity.
Summary by alphaXiv.
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