Advances in exponential random graph (p*) models

This special edition of Social Networks is argued that, due to very recent progress in the framework of exponential random graph models, the authors are now much closer to the goal of obtaining good statistical models for social networks than they have ever been before.

Abstract

User–item bipartite networks consist of users and items, where edges indicate the interactions of user–item pairs. We propose a Bayesian generative model for the user–item bipartite network that can measure the two types of rich-get-richer biases: item popularity and user influence biases. Furthermore, the model contains a novel measure of an item, namely the item quality that can be used in the item recommender system. The item quality represents the genuine worth of an item when the biases are removed. The Gibbs sampling algorithm alongside the adaptive rejection sampling is presented to obtain the posterior samples to perform the inference on the parameters. Monte Carlo simulations are performed to validate the presented algorithm. We apply the proposed model to Flickr user-tag and Netflix user–movie networks to yield remarkable interpretations of the rich-get-richer biases. We further discuss genuine item quality using Flickr tags and Netflix movies, considering the importance of bias elimination.