Figure 8:

Empirical power for rejecting the null hypothesis that two graphs have the same distribution as a function of the difference in their parameters at a 0.05 significance level (black dotted line). Both graphs are sample from a mixed-membership SBM A⁽ⁱ⁾ ~ MMSBM(Z⁽ⁱ⁾, B⁽ⁱ⁾). In the left panel, the community assignments Z⁽¹⁾ and Z⁽²⁾ are the same, while the connection probability changes on the x-axis. In the right panel, B⁽¹⁾ = B⁽²⁾, while the community assignments of a few nodes change. Both methods improve their power as the difference between the graphs get larger, but MASE can effectively use the common subspace structure to outperform OMNI when the difference between the B matrices is small. The p-values of MASE are estimated accurately usign a parametric bootstrap, while the asymptotic distribution is only valid in the first scenario when the common invariant subspace is represented in both graphs.