Graph neural networks (GNNs) are powerful models for processing graph data and have demonstrated state-of-the-art performance on many downstream tasks. However, existing GNNs can generally suffer from two limitations: over-smoothing and over-squashing, which can significantly undermine their learning ability for large graphs. To overcome these issues simultaneously, by utilizing the concept of effective resistances, we focus on minimizing total constrained resistance while identifying problematic edges using topological redundancy and bottleneck sparsity coefficients. We introduce a novel graph rewiring and preprocessing method guided by effective resistance (GPER), capable of edge addition or removal. Theoretical analysis validates our method's efficacy in mitigating over-smoothing and over-squashing. In the experiments, we conduct node and graph classifications on the benchmark datasets and can achieve an average improvement of 7.8% and 2.0%, respectively. We also conduct scalability analysis on large graphs with GCN and demonstrate that the proposed preprocess approach can reduce graph size by over 50% while improve the performance.

Link prediction is a classical problem in graph analysis with many practical applications. For directed graphs, recently developed deep learning approaches typically analyze node similarities through contrastive learning and aggregate neighborhood information through graph convolutions. In this work, we propose a novel graph neural network (GNN) framework to fuse feature embedding with community information. We theoretically demonstrate that such hybrid features can improve the performance of directed link prediction. To utilize such features efficiently, we also propose an approach to transform input graphs into directed line graphs so that nodes in the transformed graph can aggregate more information during graph convolutions. Experiments on benchmark datasets show that our approach outperforms the state-of-the-art in most cases when 30%, 40%, 50%, and 60% of the connected links are used as training data, respectively.

Graph neural networks (GNNs) with feature propagation have demonstrated their power in handling unstructured data. However, feature propagation is also a smooth process that tends to make all node representations similar as the number of propagation increases. To address this problem, we propose a novel Block-Based Adaptive Decoupling (BBAD) Framework to produce effective deep GNNs by utilizing backbone networks. In this framework, each block contains a shallow GNN with feature propagation and transformation decoupled. We also introduce layer regularizations and flexible receptive fields to automatically adjust the propagation depth and to provide different aggregation hops for each node, respectively. We prove that the traditional coupled GNNs are more likely to suffer from over-smoothing when they become deep. We also demonstrate the diversity of outputs from different blocks of our framework. In the experiments, we conduct semi-supervised and fully supervised node classifications on benchmark datasets, and the results verify that our method can not only improve the performance of various backbone networks, but also is superior to existing deep graph neural networks with less parameters.

Predicting products of organic chemical reactions is useful in chemical sciences, especially when one or more reactants are new organics. However, the performance of traditional learning models heavily relies on high-quality labeled data. In this work, to utilize unlabeled data for better prediction performance, we propose a method that combines semi-supervised learning with graph convolutional neural networks for chemical reaction prediction. First, we propose a Mean Teacher Weisfeiler–Lehman Network to find the reaction centers. Then, we construct the candidate product set. Finally, we use an Improved Weisfeiler–Lehman Difference Network to rank candidate products. Experimental results demonstrate that, with 400k labeled data, our framework can improve the top-5 accuracy by 0.7% using 35k unlabeled data. When the proportion of unlabeled data increases, the performance gain can be larger. For example, with 80k labeled data and 35k unlabeled data, the performance gain with our framework can be 1.8%.