  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.
