Abstract

Reciprocity—the tendency for directed edges to occur in mutual pairs—is a funda-mental feature of many real-world networks, yet it remains challenging to model statistically, particularly in the sparse regime. In this talk, I present a modeling framework that incorporates covariates to characterize reciprocity in directed net-works.
The first model introduces a novel Bernoulli formulation that distinguishes between reciprocal and non-reciprocal edges. We propose an associated inference procedure and provide a detailed analysis of effective sample sizes corresponding to different components of the model’s parametrization, offering insight into identifiability and estimation efficiency under sparsity.
The second model extends the classical p1 framework by incorporating link-specific reciprocity in addition to node-specific heterogeneity. We develop a new estimation approach based on a conditioning argument and derive theoretical guarantees for the resulting estimator. Numerical experiments support the theoretical findings and demonstrate the model’s practical performance.