This paper proposes a new generative model and associated link inference method based on both node popularity and similarity. The starting point for the model is the prior work in [11] where the assortative mixed-membership stochastic blockmodel (AMMSB) was presented. In the prior model, link structure is generated via community strength (via a blockmodel) and community membership. In the new work, link structure is generated by using the prior model and adding "popularity" to the generative model. After the model is presented, the authors then derive an optimization criterion based upon a variational method (since exact inference is impossible).

We develop a probabilistic approach for accurate network modeling using node popularities within the framework of the mixed-membership stochastic blockmodel (MMSB).

We develop a probabilistic approach for accurate network modeling using node popularities within the framework of the mixed-membership stochastic blockmodel (MMSB). Our model integrates some of the basic properties of nodes in social networks: homophily and preferential connection to popular nodes. We develop a scalable algorithm for posterior inference, based on a novel nonconjugate variant of stochastic variational inference. We evaluate the link prediction accuracy of our algorithm on eight real-world networks with up to 60,000 nodes, and 24 benchmark networks. We demonstrate that our algorithm predicts better than the MMSB. Further, using benchmark networks we show that node popularities are essential to achieving high accuracy in the presence of skewed degree distribution and noisy links---both characteristics of real networks.