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).

Graph Contrastive Learning (GCL) is an effective way to learn generalized graph representations in a self-supervised manner, and has grown rapidly in recent years. However, the underlying community semantics has not been well explored by most previous GCL methods. Research that attempts to leverage communities in GCL regards them as having the same influence on the graph, leading to extra representation errors. To tackle this issue, we define ''community strength'' to measure the difference of influence among communities. Under this premise, we propose a Community-Strength-enhanced Graph Contrastive Learning (CSGCL) framework to preserve community strength throughout the learning process. Firstly, we present two novel graph augmentation methods, Communal Attribute Voting (CAV) and Communal Edge Dropping (CED), where the perturbations of node attributes and edges are guided by community strength. Secondly, we propose a dynamic ''Team-up'' contrastive learning scheme, where community strength is used to progressively fine-tune the contrastive objective. We report extensive experiment results on three downstream tasks: node classification, node clustering, and link prediction. CSGCL achieves state-of-the-art performance compared with other GCL methods, validating that community strength brings effectiveness and generality to graph representations. Our code is available at https://github.com/HanChen-HUST/CSGCL.

Many important problems can be represented and studied using graphs -- social networks, interacting bacterias, brain network modules, hierarchical image clustering and many more. If we accept graphs as a basic means of structuring and analyzing data about the world, we shouldn't be surprised to see them being widely used in Machine Learning as a powerful tool that can enable intuitive properties and power a lot of useful features. Graph-based machine learning is destined to become a resilient piece of logic, transcending a lot of other techniques. This post explores the tendencies of nodes in a graph to spontaneously form clusters of internally dense linkage (hereby termed "community"); a remarkable and almost universal property of biological networks. This is particularly interesting knowing that a lot of information can be extrapolated from a node's neighbor (e.g. So how can we extract this kind of information?