Graph model selection by edge probability prequential inference.

The article introduces prequential edge probability inference, a novel statistical framework for graph model selection that represents diverse graph models as probability distributions over edges. This edge-exchangeable approach treats edges as independent and identically distributed random variables, enabling rigorous inference by leveraging multiple edge observations rather than a single graph realization, thus reducing overfitting without relying on user-defined priors. The methodology employs minimum description length principles combined with prequential inference to select optimal model parameters and hyperparameters, allowing objective comparison among models of different natures, such as stochastic blockmodels and configuration models. Applications demonstrate its effectiveness in recovering the correct number of communities in stochastic blockmodels, addressing known pitfalls like overfitting in community detection, and distinguishing between competing models even when their structural assumptions differ. The framework offers theoretical guarantees of convergence and practical advantages for analyzing complex networks where interactions arise from intertwined mechanisms.