Quantifying Network Similarity using Graph Cumulants

TL;DR

This paper introduces a novel method for comparing network distributions by converting subgraph densities into graph cumulants, demonstrating improved statistical power over traditional methods through theory, simulations, and real data applications.

Contribution

The paper proposes a new approach that transforms subgraph densities into graph cumulants for network comparison, enhancing statistical power without additional computational cost.

Findings

Graph cumulants outperform subgraph densities in hypothesis testing.

The method is validated through theoretical analysis, simulations, and real data.

Using graph cumulants improves the detection of network distribution differences.

Abstract

How might one test the hypothesis that networks were sampled from the same distribution? Here, we compare two statistical tests that use subgraph counts to address this question. The first uses the empirical subgraph densities themselves as estimates of those of the underlying distribution. The second test uses a new approach that converts these subgraph densities into estimates of the \textit{graph cumulants} of the distribution (without any increase in computational complexity). We demonstrate -- via theory, simulation, and application to real data -- the superior statistical power of using graph cumulants. In summary, when analyzing data using subgraph/motif densities, we suggest using the corresponding graph cumulants instead.