Quantifying Network Similarity using Graph Cumulants
Gecia Bravo-Hermsdorff, Lee M. Gunderson, Pierre-André Maugis, Carey E. Priebe; 24(187):1−27, 2023.
Abstract
This study compares two statistical tests that assess the hypothesis of networks being sampled from the same distribution. The first test uses the empirical subgraph densities as estimates of the underlying distribution, while the second test introduces a novel approach that converts these subgraph densities into estimates of the graph cumulants without any increase in computational complexity. Through theoretical analysis, simulations, and real data application, the study demonstrates the superior statistical power of using graph cumulants. In conclusion, when analyzing data using subgraph/motif densities, it is recommended to utilize the corresponding graph cumulants instead.
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