A Factor Model for Graph Data

Graph data have become an important channel in exploring relations among a large number of subjects in the big data era. In past decades, community structures have been found in many complex real-world networks and play a key role in the modeling of graph data, for example, the stochastic block model (SBM) and its extensions. However, recent studies have unveiled more sophisticated modules, and typical examples include star and bipartite structures. In most graph models, these link-pattern modules are piled up in terms of multiple communities. This paper proposes a graph factor model in which each node is endowed with several (latent) features. Factors are channels for edge connections and can be characterized by link functions that map features of pairs of nodes to the edge probabilities. This model may naturally incorporate different kinds of link-pattern modules including communities, stars, and bipartite structures. The inference for the model can be carried out through an Markov Chain Monte Carlo (MCMC) procedure. Both synthetic data and real-world networks are used for numerical illustrations.