Title: Nonparametric inference on network effects for relational data with dependent edges

Abstract: In recent years, the relationship network has received significant attention for its ability to provide unique insights into agent interactions across various fields. Most existing studies have primarily focused on modeling the association between the relationship network and other covariates using arguably restrictive parametric models, while largely overlooking the inference of network effects, such as the reciprocity or sender-receiver effect. Testing network effects within a relationship network is particularly challenging due to edge dependence, which renders permutation-based methods inapplicable. Our testing statistics utilize the reduced U-statistics and admit analytically tractable limiting distributions, overcoming the nontrivial sampling distributions of network moment statistics on relationship network effects caused by degeneracy and indeterminacy of degeneracy order. We establish the theoretical guarantee of our testing framework by investigating the Berry-Esseen bounds for our testing statistics. To showcase the practicality of our methods, we apply them to two real-world relationship networks, one in international trade and the other in faculty hiring networks.