This paper considers a two-sample goodness-of-fit testing problem for network data  in which the null hypothesis is that the networks are drawn from the same inhomogeneous random graph model. 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. The power properties of the tests are examined analytically, in simulation, and through two real-world applications. A key finding is that the test based on the \infty\to1 norm can be substantially more powerful than that based on the 2\to2 norm for the kinds of sparse and degree-heterogeneous networks common in economics.
How can one determine whether a community-level treatment, such as the introduction of a social program or trade shock, alters agents' incentives to form links in a network? This paper proposes analogues of a two-sample Kolmogorov-Smirnov test, widely used in the literature to test the null hypothesis of "no treatment effects", for network data . It first specifies a testing problem in which the null hypothesis is that two networks are drawn from the same random graph model. 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. Power properties of the tests are examined analytically, in simulation, and through two real-world applications. A key finding is that the test based on the \infty\to1 norm can be substantially more powerful than that based on the 2\to2 norm for the kinds of sparse and degree-heterogeneous networks common in economics.
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