Graph Convolutional Networks (GCNs) have become a standard approach for semi-supervised node classification, yet practitioners lack clear guidance on when GCNs provide meaningful improvements over simpler baselines. We present a diagnostic study using the Amazon Computers co-purchase data to understand when and why GCNs help. Through systematic experiments with simulated label scarcity, feature ablation, and per-class analysis, we find that GCN performance depends critically on the interaction between graph homophily and feature quality. GCNs provide the largest gains under extreme label scarcity, where they leverage neighborhood structure to compensate for limited supervision. Surprisingly, GCNs can match their original performance even when node features are replaced with random noise, suggesting that structure alone carries sufficient signal on highly homophilous graphs. However, GCNs hurt performance when homophily is low and features are already strong, as noisy neighbors corrupt good predictions. Our quadrant analysis reveals that GCNs help in three of four conditions and only hurt when low homophily meets strong features. These findings offer practical guidance for practitioners deciding whether to adopt graph-based methods.

Graph convolutional networks have recently gained prominence in collaborative filtering (CF) for recommendations. However, we identify potential bottlenecks in two foundational components. First, the embedding layer leads to a latent space with limited capacity, overlooking locally observed but potentially valuable preference patterns. Also, the widely-used neighborhood aggregation is limited in its ability to leverage diverse preference patterns in a fine-grained manner. Building on spectral graph theory, we reveal that these limitations stem from graph filtering with a cut-off in the frequency spectrum and a restricted linear form. To address these issues, we introduce ChebyCF, a CF framework based on graph spectral filtering. Instead of a learned embedding, it takes a user's raw interaction history to utilize the full spectrum of signals contained in it. Also, it adopts Chebyshev interpolation to effectively approximate a flexible non-linear graph filter, and further enhances it by using an additional ideal pass filter and degree-based normalization. Through extensive experiments, we verify that ChebyCF overcomes the aforementioned bottlenecks and achieves state-of-the-art performance across multiple benchmarks and reasonably fast inference. Our code is available at https://github.com/chanwoo0806/ChebyCF.

Graph Neural Networks (GNNs) have become the leading approach for addressing graph analytical problems in various real-world scenarios. However, GNNs may produce biased predictions against certain demographic subgroups due to node attributes and neighbors surrounding a node. Most current research on GNN fairness focuses predominantly on debiasing GNNs using oversimplified fairness evaluation metrics, which can give a misleading impression of fairness. Understanding the potential evaluation paradoxes due to the complicated nature of the graph structure is crucial for developing effective GNN debiasing mechanisms. In this paper, we examine the effectiveness of current GNN debiasing methods in terms of unfairness evaluation. Specifically, we introduce a community-level strategy to measure bias in GNNs and evaluate debiasing methods at this level. Further, We introduce ComFairGNN, a novel framework designed to mitigate community-level bias in GNNs. Our approach employs a learnable coreset-based debiasing function that addresses bias arising from diverse local neighborhood distributions during GNNs neighborhood aggregation. Comprehensive evaluations on three benchmark datasets demonstrate our model's effectiveness in both accuracy and fairness metrics.

We delve into the issue of node classification within graphs, specifically reevaluating the concept of neighborhood aggregation, which is a fundamental component in graph neural networks (GNNs). Our analysis reveals conceptual flaws within certain benchmark GNN models when operating under the assumption of edge-independent node labels, a condition commonly observed in benchmark graphs employed for node classification. Approaching neighborhood aggregation from a statistical signal processing perspective, our investigation provides novel insights which may be used to design more efficient GNN models.

A critical aspect of Graph Neural Networks (GNNs) is to enhance the node representations by aggregating node neighborhood information. However, when detecting anomalies, the representations of abnormal nodes are prone to be averaged by normal neighbors, making the learned anomaly representations less distinguishable. To tackle this issue, we propose CAGAD -- an unsupervised Counterfactual data Augmentation method for Graph Anomaly Detection -- which introduces a graph pointer neural network as the heterophilic node detector to identify potential anomalies whose neighborhoods are normal-node-dominant. For each identified potential anomaly, we design a graph-specific diffusion model to translate a part of its neighbors, which are probably normal, into anomalous ones. At last, we involve these translated neighbors in GNN neighborhood aggregation to produce counterfactual representations of anomalies. Through aggregating the translated anomalous neighbors, counterfactual representations become more distinguishable and further advocate detection performance. The experimental results on four datasets demonstrate that CAGAD significantly outperforms strong baselines, with an average improvement of 2.35% on F1, 2.53% on AUC-ROC, and 2.79% on AUC-PR.

Graph Attention Networks (GATs) are designed to provide flexible neighborhood aggregation that assigns weights to neighbors according to their importance. In practice, however, GATs are often unable to switch off task-irrelevant neighborhood aggregation, as we show experimentally and analytically. To address this challenge, we propose GATE, a GAT extension that holds three major advantages: i) It alleviates over-smoothing by addressing its root cause of unnecessary neighborhood aggregation. ii) Similarly to perceptrons, it benefits from higher depth as it can still utilize additional layers for (non-)linear feature transformations in case of (nearly) switched-off neighborhood aggregation. iii) By down-weighting connections to unrelated neighbors, it often outperforms GATs on real-world heterophilic datasets. To further validate our claims, we construct a synthetic test bed to analyze a model's ability to utilize the appropriate amount of neighborhood aggregation, which could be of independent interest.

Conventional graph neural networks (GNNs) are often confronted with fairness issues that may stem from their input, including node attributes and neighbors surrounding a node. While several recent approaches have been proposed to eliminate the bias rooted in sensitive attributes, they ignore the other key input of GNNs, namely the neighbors of a node, which can introduce bias since GNNs hinge on neighborhood structures to generate node representations. In particular, the varying neighborhood structures across nodes, manifesting themselves in drastically different node degrees, give rise to the diverse behaviors of nodes and biased outcomes. In this paper, we first define and generalize the degree bias using a generalized definition of node degree as a manifestation and quantification of different multi-hop structures around different nodes. To address the bias in the context of node classification, we propose a novel GNN framework called Generalized Degree Fairness-centric Graph Neural Network (Deg-FairGNN). Specifically, in each GNN layer, we employ a learnable debiasing function to generate debiasing contexts, which modulate the layer-wise neighborhood aggregation to eliminate the degree bias originating from the diverse degrees among nodes. Extensive experiments on three benchmark datasets demonstrate the effectiveness of our model on both accuracy and fairness metrics.

Graph Convolutional Networks (GCNs) and their variants have achieved significant performances on various recommendation tasks. However, many existing GCN models tend to perform recursive aggregations among all related nodes, which can arise severe computational burden to hinder their application to large-scale recommendation tasks. To this end, this paper proposes the flattened GCN~(FlatGCN) model, which is able to achieve superior performance with remarkably less complexity compared with existing models. Our main contribution is three-fold. First, we propose a simplified but powerful GCN architecture which aggregates the neighborhood information using one flattened GCN layer, instead of recursively. The aggregation step in FlatGCN is parameter-free such that it can be pre-computed with parallel computation to save memory and computational cost. Second, we propose an informative neighbor-infomax sampling method to select the most valuable neighbors by measuring the correlation among neighboring nodes based on a principled metric. Third, we propose a layer ensemble technique which improves the expressiveness of the learned representations by assembling the layer-wise neighborhood representations at the final layer. Extensive experiments on three datasets verify that our proposed model outperforms existing GCN models considerably and yields up to a few orders of magnitude speedup in training efficiency.

Graph kernel approaches have typically been the most popular strategy for graph classification tasks. Graph kernels can be thought of as functions that measure the similarity of two graphs. They allow kernelized learning algorithms like support vector machines to work directly on charts rather than convert them to fixed-length, real-valued feature vectors through feature extraction. In recent years, the use of Graph Neural Networks (GNNs) based on high-performance message-passing neural networks has exploded (MPNNs). As a result, they've grown increasingly popular for graph categorization.

We focus on graph classification using a graph neural network (GNN) model that precomputes the node features using a bank of neighborhood aggregation graph operators arranged in parallel. These GNN models have a natural advantage of reduced training and inference time due to the precomputations but are also fundamentally different from popular GNN variants that update node features through a sequential neighborhood aggregation procedure during training. We provide theoretical conditions under which a generic GNN model with parallel neighborhood aggregations (PA-GNNs, in short) are provably as powerful as the well-known Weisfeiler-Lehman (WL) graph isomorphism test in discriminating non-isomorphic graphs. Although PA-GNN models do not have an apparent relationship with the WL test, we show that the graph embeddings obtained from these two methods are injectively related. We then propose a specialized PA-GNN model, called SPIN, which obeys the developed conditions. We demonstrate via numerical experiments that the developed model achieves state-of-the-art performance on many diverse real-world datasets while maintaining the discriminative power of the WL test and the computational advantage of preprocessing graphs before the training process.