Permutation and randomization tests for network analysis

•Permutation tests yield casual interpretations when combined with random assignment.•Permutation tests provide high power against many network generation models.•Test statistics account for edges, clustering, and centrality.•Significant effects found for gene expression consistent with a latent space model.•Female corporate board membership consistent with a scale free network. Permutation tests have a long history in testing hypotheses of independence between nodal attributes and network structure, though they are often thought less informative than parametric modeling techniques. In this paper, we show that when the nodal attribute is random assignment to a treatment condition, permutation tests provide a valid test of the causal effect of treatment. We discuss existing test statistics used in network permutation tests and propose several new statistics. In simulations we find that these statistics perform well compared to parametric tests and that specific statistics can be selected to provide power against common network models. We illustrate the methods with gene-wide association study performed on randomized study participants and an observational study of gender membership on Scandinavian corporate boards.