Our study aims to promote a higher standard of empirical rigor in the field of graph machine learning, encouraging more accurate comparisons and evaluations of model capabilities.

Graph Neural Networks (GNNs) have been shown to achieve remarkable performance on node classification tasks by exploiting both graph structures and node features. The majority of existing GNNs rely on the implicit homophily assumption. Recent studies have demonstrated that GNNs may struggle to model heterophilous graphs where nodes with different labels are more likely connected. To address this issue, we propose a generic GNN applicable to both homophilous and heterophilous graphs, namely Low-Rank Graph Neural Network (LRGNN). Our analysis demonstrates that a signed graph's global label relationship matrix has a low rank. This insight inspires us to predict the label relationship matrix by solving a robust low-rank matrix approximation problem, as prior research has proven that low-rank approximation could achieve perfect recovery under certain conditions. The experimental results reveal that the solution bears a strong resemblance to the label relationship matrix, presenting two advantages for graph modeling: a block diagonal structure and varying distributions of within-class and between-class entries.

Our study aims to promote a higher standard of empirical rigor in the field of graph machine learning, encouraging more accurate comparisons and evaluations of model capabilities.

Homophily is a graph property describing the tendency of edges to connect similar nodes; the opposite is called heterophily .

Graph Neural Networks (GNNs) have demonstrated significant success in learning from graph-structured data but often struggle on heterophilous graphs, where connected nodes differ in features or class labels. This limitation arises from indiscriminate neighbor aggregation and insufficient incorporation of higher-order structural patterns. To address these challenges, we propose GLANCE (Graph Logic Attention Network with Cluster Enhancement), a novel framework that integrates logic-guided reasoning, dynamic graph refinement, and adaptive clustering to enhance graph representation learning. GLANCE combines a logic layer for interpretable and structured embeddings, multi-head attention-based edge pruning for denoising graph structures, and clustering mechanisms for capturing global patterns. Experimental results in benchmark datasets, including Cornell, Texas, and Wisconsin, demonstrate that GLANCE achieves competitive performance, offering robust and interpretable solutions for heterophilous graph scenarios. The proposed framework is lightweight, adaptable, and uniquely suited to the challenges of heterophilous graphs.

Multi-view clustering is an important machine learning task for multi-media data, encompassing various domains such as images, videos, and texts. Moreover, with the growing abundance of graph data, the significance of multi-view graph clustering (MVGC) has become evident. Most existing methods focus on graph neural networks (GNNs) to extract information from both graph structure and feature data to learn distinguishable node representations. However, traditional GNNs are designed with the assumption of homophilous graphs, making them unsuitable for widely prevalent heterophilous graphs. Several techniques have been introduced to enhance GNNs for heterophilous graphs. While these methods partially mitigate the heterophilous graph issue, they often neglect the advantages of traditional GNNs, such as their simplicity, interpretability, and efficiency. In this paper, we propose a novel multi-view graph clustering method based on dual-optimized adaptive graph reconstruction, named DOAGC. It mainly aims to reconstruct the graph structure adapted to traditional GNNs to deal with heterophilous graph issues while maintaining the advantages of traditional GNNs. Specifically, we first develop an adaptive graph reconstruction mechanism that accounts for node correlation and original structural information. To further optimize the reconstruction graph, we design a dual optimization strategy and demonstrate the feasibility of our optimization strategy through mutual information theory. Numerous experiments demonstrate that DOAGC effectively mitigates the heterophilous graph problem.

Graph Neural Networks (GNNs) have been shown to achieve remarkable performance on node classification tasks by exploiting both graph structures and node features. The majority of existing GNNs rely on the implicit homophily assumption. Recent studies have demonstrated that GNNs may struggle to model heterophilous graphs where nodes with different labels are more likely connected. To address this issue, we propose a generic GNN applicable to both homophilous and heterophilous graphs, namely Low-Rank Graph Neural Network (LRGNN). Our analysis demonstrates that a signed graph's global label relationship matrix has a low rank.

With the increasing prevalence of graph-structured data, multi-view graph clustering has been widely used in various downstream applications. Existing approaches primarily rely on a unified message passing mechanism, which significantly enhances clustering performance. Nevertheless, this mechanism limits its applicability to heterophilous situations, as it is fundamentally predicated on the assumption of homophily, i.e., the connected nodes often belong to the same class. In reality, this assumption does not always hold; a moderately or even mildly homophilous graph is more common than a fully homophilous one due to inevitable heterophilous information in the graph. To address this issue, in this paper, we propose a novel SiMilarity-enhanced Homophily for Multi-view Heterophilous Graph Clustering (SMHGC) approach. By analyzing the relationship between similarity and graph homophily, we propose to enhance the homophily by introducing three similarity terms, i.e., neighbor pattern similarity, node feature similarity, and multi-view global similarity, in a label-free manner. Then, a consensus-based inter- and intra-view fusion paradigm is proposed to fuse the improved homophilous graph from different views and utilize them for clustering. The state-of-the-art experimental results on both multi-view heterophilous and homophilous datasets collectively demonstrate the strong capacity of similarity for unsupervised multi-view heterophilous graph learning. Additionally, the consistent performance across semi-synthetic datasets with varying levels of homophily serves as further evidence of SMHGC's resilience to heterophily.

Graph Transformers (GTs) have recently emerged as popular alternatives to traditional message-passing Graph Neural Networks (GNNs), due to their theoretically superior expressiveness and impressive performance reported on standard node classification benchmarks, often significantly outperforming GNNs. In this paper, we conduct a thorough empirical analysis to reevaluate the performance of three classic GNN models (GCN, GAT, and GraphSAGE) against GTs. Our findings suggest that the previously reported superiority of GTs may have been overstated due to suboptimal hyperparameter configurations in GNNs. Remarkably, with slight hyperparameter tuning, these classic GNN models achieve state-of-the-art performance, matching or even exceeding that of recent GTs across 17 out of the 18 diverse datasets examined. Additionally, we conduct detailed ablation studies to investigate the influence of various GNN configurations, such as normalization, dropout, residual connections, network depth, and jumping knowledge mode, on node classification performance. Our study aims to promote a higher standard of empirical rigor in the field of graph machine learning, encouraging more accurate comparisons and evaluations of model capabilities.

Graph Neural Networks (GNNs) have demonstrated strong performance in graph mining tasks due to their message-passing mechanism, which is aligned with the homophily assumption that adjacent nodes exhibit similar behaviors. However, in many real-world graphs, connected nodes may display contrasting behaviors, termed as heterophilous patterns, which has attracted increased interest in heterophilous GNNs (HTGNNs). Although the message-passing mechanism seems unsuitable for heterophilous graphs due to the propagation of class-irrelevant information, it is still widely used in many existing HTGNNs and consistently achieves notable success. This raises the question: why does message passing remain effective on heterophilous graphs? To answer this question, in this paper, we revisit the message-passing mechanisms in heterophilous graph neural networks and reformulate them into a unified heterophilious message-passing (HTMP) mechanism. Based on HTMP and empirical analysis, we reveal that the success of message passing in existing HTGNNs is attributed to implicitly enhancing the compatibility matrix among classes. Moreover, we argue that the full potential of the compatibility matrix is not completely achieved due to the existence of incomplete and noisy semantic neighborhoods in real-world heterophilous graphs. To bridge this gap, we introduce a new approach named CMGNN, which operates within the HTMP mechanism to explicitly leverage and improve the compatibility matrix. A thorough evaluation involving 10 benchmark datasets and comparative analysis against 13 well-established baselines highlights the superior performance of the HTMP mechanism and CMGNN method.