Statistical Inference for Dynamic Networks Based on Degree Heterogeneity

Interactions among actors may undergo dynamic systemic changes. A model called the degree‐corrected network matrix autoregression (DCNMA) model is proposed to analyse dynamic networks and predict dynamic clustering. Built upon the degree‐corrected mixed membership (DCMM) model, this model considers not only the mixture of roles and degree heterogeneity but also autoregressive community membership probabilities. In the absence of degree heterogeneity, a simplified model called the mixed membership network matrix autoregression (MMNMA) model has also been proposed. Hypothesis tests are performed to assess the dynamic membership of participants, and the sampling distribution is inferred using bootstrap. The relevant theories are established, and the procedures are compared with existing methods on synthetic datasets. DCNMA and MMNMA show good clustering performance on two dynamic social network datasets.