Before revision:  It first outlines a randomization test for the null hypothesis that controls size in finite samples based on any test statistic. It then focuses on two particular statistics that produce tests powerful against a large class of alternative hypotheses. The statistics are based on the magnitude of the difference between the networks' adjacency matrices as measured by the 2\to2 and \infty\to1 operator norms.
After revision:  It then describes two randomization tests based on the magnitude of the difference between the networks' adjacency matrices as measured by the 2\to2 and \infty\to1 operator norms.