Multi-relational networks capture intricate relationships in data and have diverse applications across fields such as biomedical, financial, and social sciences. As networks derived from increasingly large datasets become more common, identifying efficient methods for representing and analyzing them becomes crucial. This work extends the Prime Adjacency Matrices (PAMs) framework, which employs prime numbers to represent distinct relations within a network uniquely. This enables a compact representation of a complete multi-relational graph using a single adjacency matrix, which, in turn, facilitates quick computation of multi-hop adjacency matrices. In this work, we enhance the framework by introducing a lossless algorithm for calculating the multi-hop matrices and propose the Bag of Paths (BoP) representation, a versatile feature extraction methodology for various graph analytics tasks, at the node, edge, and graph level. We demonstrate the efficiency of the framework across various tasks and datasets, showing that simple BoP-based models perform comparably to or better than commonly used neural models while offering improved speed and interpretability.
Graph Neural Networks (GNNs) have been widely employed for semi-supervised node classification tasks on graphs. However, the performance of GNNs is significantly affected by label noise, that is, a small amount of incorrectly labeled nodes can substantially misguide model training. Mainstream solutions define node classification with label noise (NCLN) as a reliable labeling task, often introducing node similarity with quadratic computational complexity to more accurately assess label reliability. To this end, in this paper, we introduce the Label Ensemble Graph Neural Network (LEGNN), a lower complexity method for robust GNNs training against label noise. LEGNN reframes NCLN as a label ensemble task, gathering informative multiple labels instead of constructing a single reliable label, avoiding high-complexity computations for reliability assessment. Specifically, LEGNN conducts a two-step process: bootstrapping neighboring contexts and robust learning with gathered multiple labels. In the former step, we apply random neighbor masks for each node and gather the predicted labels as a high-probability label set. This mitigates the impact of inaccurately labeled neighbors and diversifies the label set. In the latter step, we utilize a partial label learning based strategy to aggregate the high-probability label information for model training. Additionally, we symmetrically gather a low-probability label set to counteract potential noise from the bootstrapped high-probability label set. Extensive experiments on six datasets demonstrate that LEGNN achieves outstanding performance while ensuring efficiency. Moreover, it exhibits good scalability on dataset with over one hundred thousand nodes and one million edges.
This paper addresses domain adaptation challenges in graph data resulting from chronological splits. In a transductive graph learning setting, where each node is associated with a timestamp, we focus on the task of Semi-Supervised Node Classification (SSNC), aiming to classify recent nodes using labels of past nodes. Temporal dependencies in node connections create domain shifts, causing significant performance degradation when applying models trained on historical data into recent data. Given the practical relevance of this scenario, addressing domain adaptation in chronological split data is crucial, yet underexplored. We propose Imposing invariance with Message Passing in Chronological split Temporal Graphs (IMPaCT), a method that imposes invariant properties based on realistic assumptions derived from temporal graph structures. Unlike traditional domain adaptation approaches which rely on unverifiable assumptions, IMPaCT explicitly accounts for the characteristics of chronological splits. The IMPaCT is further supported by rigorous mathematical analysis, including a derivation of an upper bound of the generalization error. Experimentally, IMPaCT achieves a 3.8% performance improvement over current SOTA method on the ogbn-mag graph dataset. Additionally, we introduce the Temporal Stochastic Block Model (TSBM), which replicates temporal graphs under varying conditions, demonstrating the applicability of our methods to general spatial GNNs.
Graph Neural Networks (GNNs) have advanced relational data analysis but lack invariance learning techniques common in image classification. In node classification with GNNs, it is actually the ego-graph of the center node that is classified. This research extends the scale invariance concept to node classification by drawing an analogy to image processing: just as scale invariance being used in image classification to capture multi-scale features, we propose the concept of ``scaled ego-graphs''. Scaled ego-graphs generalize traditional ego-graphs by replacing undirected single-edges with ``scaled-edges'', which are ordered sequences of multiple directed edges. We empirically assess the performance of the proposed scale invariance in graphs on seven benchmark datasets, across both homophilic and heterophilic structures. Our scale-invariance-based graph learning outperforms inception models derived from random walks by being simpler, faster, and more accurate. The scale invariance explains inception models' success on homophilic graphs and limitations on heterophilic graphs. To ensure applicability of inception model to heterophilic graphs as well, we further present ScaleNet, an architecture that leverages multi-scaled features. ScaleNet achieves state-of-the-art results on five out of seven datasets (four homophilic and one heterophilic) and matches top performance on the remaining two, demonstrating its excellent applicability. This represents a significant advance in graph learning, offering a unified framework that enhances node classification across various graph types. Our code is available at https://github.com/Qin87/ScaleNet/tree/July25.
Recent papers in the graph machine learning literature have introduced a number of approaches for hyperbolic representation learning. The asserted benefits are improved performance on a variety of graph tasks, node classification and link prediction included. Claims have also been made about the geometric suitability of particular hierarchical graph datasets to representation in hyperbolic space. Despite these claims, our work makes a surprising discovery: when simple Euclidean models with comparable numbers of parameters are properly trained in the same environment, in most cases, they perform as well, if not better, than all introduced hyperbolic graph representation learning models, even on graph datasets previously claimed to be the most hyperbolic as measured by Gromov $\delta$-hyperbolicity (i.e., perfect trees). This observation gives rise to a simple question: how can this be? We answer this question by taking a careful look at the field of hyperbolic graph representation learning as it stands today, and find that a number of papers fail to diligently present baselines, make faulty modelling assumptions when constructing algorithms, and use misleading metrics to quantify geometry of graph datasets. We take a closer look at each of these three problems, elucidate the issues, perform an analysis of methods, and introduce a parametric family of benchmark datasets to ascertain the applicability of (hyperbolic) graph neural networks.
Node classification with Graph Neural Networks (GNN) under a fixed set of labels is well known in contrast to Graph Few-Shot Class Incremental Learning (GFSCIL), which involves learning a GNN classifier as graph nodes and classes growing over time sporadically. We introduce inductive GFSCIL that continually learns novel classes with newly emerging nodes while maintaining performance on old classes without accessing previous data. This addresses the practical concern of transductive GFSCIL, which requires storing the entire graph with historical data. Compared to the transductive GFSCIL, the inductive setting exacerbates catastrophic forgetting due to inaccessible previous data during incremental training, in addition to overfitting issue caused by label sparsity. Thus, we propose a novel method, called Topology-based class Augmentation and Prototype calibration (TAP). To be specific, it first creates a triple-branch multi-topology class augmentation method to enhance model generalization ability. As each incremental session receives a disjoint subgraph with nodes of novel classes, the multi-topology class augmentation method helps replicate such a setting in the base session to boost backbone versatility. In incremental learning, given the limited number of novel class samples, we propose an iterative prototype calibration to improve the separation of class prototypes. Furthermore, as backbone fine-tuning poses the feature distribution drift, prototypes of old classes start failing over time, we propose the prototype shift method for old classes to compensate for the drift. We showcase the proposed method on four datasets.
The rapid expansion of Internet of Things (IoT) has resulted in vast, heterogeneous graphs that capture complex interactions among devices, sensors, and systems. Efficient analysis of these graphs is critical for deriving insights in IoT scenarios such as smart cities, industrial IoT, and intelligent transportation systems. However, the scale and diversity of IoT-generated data present significant challenges, and existing methods often struggle with preserving the structural integrity and semantic richness of these complex graphs. Many current approaches fail to maintain the balance between computational efficiency and the quality of the insights generated, leading to potential loss of critical information necessary for accurate decision-making in IoT applications. We introduce HeteroSample, a novel sampling method designed to address these challenges by preserving the structural integrity, node and edge type distributions, and semantic patterns of IoT-related graphs. HeteroSample works by incorporating the novel top-leader selection, balanced neighborhood expansion, and meta-path guided sampling strategies. The key idea is to leverage the inherent heterogeneous structure and semantic relationships encoded by meta-paths to guide the sampling process. This approach ensures that the resulting subgraphs are representative of the original data while significantly reducing computational overhead. Extensive experiments demonstrate that HeteroSample outperforms state-of-the-art methods, achieving up to 15% higher F1 scores in tasks such as link prediction and node classification, while reducing runtime by 20%.These advantages make HeteroSample a transformative tool for scalable and accurate IoT applications, enabling more effective and efficient analysis of complex IoT systems, ultimately driving advancements in smart cities, industrial IoT, and beyond.
Incremental graph learning has gained significant attention for its ability to address the catastrophic forgetting problem in graph representation learning. However, traditional methods often rely on a large number of labels for node classification, which is impractical in real-world applications. This makes few-shot incremental learning on graphs a pressing need. Current methods typically require extensive training samples from meta-learning to build memory and perform intensive fine-tuning of GNN parameters, leading to high memory consumption and potential loss of previously learned knowledge. To tackle these challenges, we introduce Mecoin, an efficient method for building and maintaining memory. Mecoin employs Structured Memory Units to cache prototypes of learned categories, as well as Memory Construction Modules to update these prototypes for new categories through interactions between the nodes and the cached prototypes. Additionally, we have designed a Memory Representation Adaptation Module to store probabilities associated with each class prototype, reducing the need for parameter fine-tuning and lowering the forgetting rate. When a sample matches its corresponding class prototype, the relevant probabilities are retrieved from the MRaM. Knowledge is then distilled back into the GNN through a Graph Knowledge Distillation Module, preserving the model's memory. We analyze the effectiveness of Mecoin in terms of generalization error and explore the impact of different distillation strategies on model performance through experiments and VC-dimension analysis. Compared to other related works, Mecoin shows superior performance in accuracy and forgetting rate. Our code is publicly available on the https://github.com/Arvin0313/Mecoin-GFSCIL.git .
Graph neural networks (GNNs) have become essential tools for analyzing non-Euclidean data across various domains. During training stage, sampling plays an important role in reducing latency by limiting the number of nodes processed, particularly in large-scale applications. However, as the demand for better prediction performance grows, existing sampling algorithms become increasingly complex, leading to significant overhead. To mitigate this, we propose YOSO (You-Only-Sample-Once), an algorithm designed to achieve efficient training while preserving prediction accuracy. YOSO introduces a compressed sensing (CS)-based sampling and reconstruction framework, where nodes are sampled once at input layer, followed by a lossless reconstruction at the output layer per epoch. By integrating the reconstruction process with the loss function of specific learning tasks, YOSO not only avoids costly computations in traditional compressed sensing (CS) methods, such as orthonormal basis calculations, but also ensures high-probability accuracy retention which equivalent to full node participation. Experimental results on node classification and link prediction demonstrate the effectiveness and efficiency of YOSO, reducing GNN training by an average of 75\% compared to state-of-the-art methods, while maintaining accuracy on par with top-performing baselines.
Graph Neural Networks (GNNs), which are nowadays the benchmark approach in graph representation learning, have been shown to be vulnerable to adversarial attacks, raising concerns about their real-world applicability. While existing defense techniques primarily concentrate on the training phase of GNNs, involving adjustments to message passing architectures or pre-processing methods, there is a noticeable gap in methods focusing on increasing robustness during inference. In this context, this study introduces RobustCRF, a post-hoc approach aiming to enhance the robustness of GNNs at the inference stage. Our proposed method, founded on statistical relational learning using a Conditional Random Field, is model-agnostic and does not require prior knowledge about the underlying model architecture. We validate the efficacy of this approach across various models, leveraging benchmark node classification datasets.
Graph Neural Networks (GNNs) have shown great promise in modeling relationships between nodes in a graph, but capturing higher-order relationships remains a challenge for large-scale networks. Previous studies have primarily attempted to utilize the information from higher-order neighbors in the graph, involving the incorporation of powers of the shift operator, such as the graph Laplacian or adjacency matrix. This approach comes with a trade-off in terms of increased computational and memory demands. Relying on graph spectral theory, we make a fundamental observation: the regular and the Hadamard power of the Laplacian matrix behave similarly in the spectrum. This observation has significant implications for capturing higher-order information in GNNs for various tasks such as node classification and semi-supervised learning. Consequently, we propose a novel graph convolutional operator based on the sparse Sobolev norm of graph signals. Our approach, known as Sparse Sobolev GNN (S2-GNN), employs Hadamard products between matrices to maintain the sparsity level in graph representations. S2-GNN utilizes a cascade of filters with increasing Hadamard powers to generate a diverse set of functions. We theoretically analyze the stability of S2-GNN to show the robustness of the model against possible graph perturbations. We also conduct a comprehensive evaluation of S2-GNN across various graph mining, semi-supervised node classification, and computer vision tasks. In particular use cases, our algorithm demonstrates competitive performance compared to state-of-the-art GNNs in terms of performance and running time.
Graph neural networks (GNNs) are prominent for their effectiveness in processing graph data for semi-supervised node classification tasks. Most works of GNNs assume that the observed structure accurately represents the underlying node relationships. However, the graph structure is inevitably noisy or incomplete in reality, which can degrade the quality of graph representations. Therefore, it is imperative to learn a clean graph structure that balances performance and robustness. In this paper, we propose a novel method named \textit{Global-augmented Graph Structure Learning} (GaGSL), guided by the Graph Information Bottleneck (GIB) principle. The key idea behind GaGSL is to learn a compact and informative graph structure for node classification tasks. Specifically, to mitigate the bias caused by relying solely on the original structure, we first obtain augmented features and augmented structure through global feature augmentation and global structure augmentation. We then input the augmented features and augmented structure into a structure estimator with different parameters for optimization and re-definition of the graph structure, respectively. The redefined structures are combined to form the final graph structure. Finally, we employ GIB based on mutual information to guide the optimization of the graph structure to obtain the minimum sufficient graph structure. Comprehensive evaluations across a range of datasets reveal the outstanding performance and robustness of GaGSL compared with the state-of-the-art methods.
Graph Neural Networks (GNNs) have gained considerable prominence in semi-supervised learning tasks in processing graph-structured data, primarily owing to their message-passing mechanism, which largely relies on the availability of clean labels. However, in real-world scenarios, labels on nodes of graphs are inevitably noisy and sparsely labeled, significantly degrading the performance of GNNs. Exploring robust GNNs for semi-supervised node classification in the presence of noisy and sparse labels remains a critical challenge. Therefore, we propose a novel \textbf{G}raph \textbf{N}eural \textbf{N}etwork with \textbf{C}oarse- and \textbf{F}ine-\textbf{G}rained \textbf{D}ivision for mitigating label sparsity and noise, namely GNN-CFGD. The key idea of GNN-CFGD is reducing the negative impact of noisy labels via coarse- and fine-grained division, along with graph reconstruction. Specifically, we first investigate the effectiveness of linking unlabeled nodes to cleanly labeled nodes, demonstrating that this approach is more effective in combating labeling noise than linking to potentially noisy labeled nodes. Based on this observation, we introduce a Gaussian Mixture Model (GMM) based on the memory effect to perform a coarse-grained division of the given labels into clean and noisy labels. Next, we propose a clean labels oriented link that connects unlabeled nodes to cleanly labeled nodes, aimed at mitigating label sparsity and promoting supervision propagation. Furthermore, to provide refined supervision for noisy labeled nodes and additional supervision for unlabeled nodes, we fine-grain the noisy labeled and unlabeled nodes into two candidate sets based on confidence, respectively. Extensive experiments on various datasets demonstrate the superior effectiveness and robustness of GNN-CFGD.
Despite the successful application of Temporal Graph Networks (TGNs) for tasks such as dynamic node classification and link prediction, they still perform poorly on the task of dynamic node affinity prediction -- where the goal is to predict 'how much' two nodes will interact in the future. In fact, simple heuristic approaches such as persistent forecasts and moving averages over ground-truth labels significantly and consistently outperform TGNs. Building on this observation, we find that computing heuristics over messages is an equally competitive approach, outperforming TGN and all current temporal graph (TG) models on dynamic node affinity prediction. In this paper, we prove that no formulation of TGN can represent persistent forecasting or moving averages over messages, and propose to enhance the expressivity of TGNs by adding source-target identification to each interaction event message. We show that this modification is required to represent persistent forecasting, moving averages, and the broader class of autoregressive models over messages. Our proposed method, TGNv2, significantly outperforms TGN and all current TG models on all Temporal Graph Benchmark (TGB) dynamic node affinity prediction datasets.
Graph Convolutional Network (GCN) are widely used in Graph Anomaly Detection (GAD) due to their natural compatibility with graph structures, resulting in significant performance improvements. However, most researchers approach GAD as a graph node classification task and often rely on low-pass filters or feature aggregation from neighboring nodes. This paper proposes a novel approach by introducing a High-Pass Graph Convolution Network (HP-GCN) for GAD. The proposed HP-GCN leverages high-frequency components to detect anomalies, as anomalies tend to increase high-frequency signals within the network of normal nodes. Additionally, isolated nodes, which lack interactions with other nodes, present a challenge for Graph Neural Network (GNN). To address this, the model segments the graph into isolated nodes and nodes within connected subgraphs. Isolated nodes learn their features through Multi-Layer Perceptron (MLP), enhancing detection accuracy. The model is evaluated and validated on YelpChi, Amazon, T-Finance, and T-Social datasets. The results showed that the proposed HP-GCN can achieve anomaly detection accuracy of 96.10%, 98.16%, 96.46%, and 98.94%, respectively. The findings demonstrate that the HP-GCN outperforms existing GAD methods based on spatial domain GNN as well as those using low-pass and band-pass filters in spectral domain GCN. The findings underscore the effectiveness of this method in improving anomaly detection performance. Source code can be found at: https://github.com/meteor0033/High-pass_GAD.git.
Graphs play a central role in modeling complex relationships across various domains. Most graph learning methods rely heavily on neighborhood information, raising the question of how to handle cold-start nodes - nodes with no known connections within the graph. These models often overlook the cold-start nodes, making them ineffective for real-world scenarios. To tackle this, we propose G-SPARC, a novel framework addressing cold-start nodes, that leverages generalizable spectral embedding. This framework enables extension to state-of-the-art methods making them suitable for practical applications. By utilizing a key idea of transitioning from graph representation to spectral representation, our approach is generalizable to cold-start nodes, capturing the global structure of the graph without relying on adjacency data. Experimental results demonstrate that our method outperforms existing models on cold-start nodes across various tasks like node classification, node clustering, and link prediction. G-SPARC provides a breakthrough built-in solution to the cold-start problem in graph learning. Our code will be publicly available upon acceptance.
Graph Neural Networks (GNNs) have become essential in interpreting relational data across various domains, yet, they often struggle to generalize to unseen graph data that differs markedly from training instances. In this paper, we introduce a novel framework called General Retrieval-Augmented Graph Learning (RAGraph), which brings external graph data into the general graph foundation model to improve model generalization on unseen scenarios. On the top of our framework is a toy graph vector library that we established, which captures key attributes, such as features and task-specific label information. During inference, the RAGraph adeptly retrieves similar toy graphs based on key similarities in downstream tasks, integrating the retrieved data to enrich the learning context via the message-passing prompting mechanism. Our extensive experimental evaluations demonstrate that RAGraph significantly outperforms state-of-the-art graph learning methods in multiple tasks such as node classification, link prediction, and graph classification across both dynamic and static datasets. Furthermore, extensive testing confirms that RAGraph consistently maintains high performance without the need for task-specific fine-tuning, highlighting its adaptability, robustness, and broad applicability.
Graph Neural Networks (GNNs) are susceptible to distribution shifts, creating vulnerability and security issues in critical domains. There is a pressing need to enhance the generalizability of GNNs on out-of-distribution (OOD) test data. Existing methods that target learning an invariant (feature, structure)-label mapping often depend on oversimplified assumptions about the data generation process, which do not adequately reflect the actual dynamics of distribution shifts in graphs. In this paper, we introduce a more realistic graph data generation model using Structural Causal Models (SCMs), allowing us to redefine distribution shifts by pinpointing their origins within the generation process. Building on this, we propose a casual decoupling framework, DeCaf, that independently learns unbiased feature-label and structure-label mappings. We provide a detailed theoretical framework that shows how our approach can effectively mitigate the impact of various distribution shifts. We evaluate DeCaf across both real-world and synthetic datasets that demonstrate different patterns of shifts, confirming its efficacy in enhancing the generalizability of GNNs.
Graph Neural Networks (GNN) exhibit superior performance in graph representation learning, but their inference cost can be high, due to an aggregation operation that can require a memory fetch for a very large number of nodes. This inference cost is the major obstacle to deploying GNN models with \emph{online prediction} to reflect the potentially dynamic node features. To address this, we propose an approach to reduce the number of nodes that are included during aggregation. We achieve this through a sparse decomposition, learning to approximate node representations using a weighted sum of linearly transformed features of a carefully selected subset of nodes within the extended neighbourhood. The approach achieves linear complexity with respect to the average node degree and the number of layers in the graph neural network. We introduce an algorithm to compute the optimal parameters for the sparse decomposition, ensuring an accurate approximation of the original GNN model, and present effective strategies to reduce the training time and improve the learning process. We demonstrate via extensive experiments that our method outperforms other baselines designed for inference speedup, achieving significant accuracy gains with comparable inference times for both node classification and spatio-temporal forecasting tasks.
Graph condensation has emerged as a promising avenue to enable scalable training of GNNs by compressing the training dataset while preserving essential graph characteristics. Our study uncovers significant shortcomings in current graph condensation techniques. First, the majority of the algorithms paradoxically require training on the full dataset to perform condensation. Second, due to their gradient-emulating approach, these methods require fresh condensation for any change in hyperparameters or GNN architecture, limiting their flexibility and reusability. Finally, they fail to achieve substantial size reduction due to synthesizing fully-connected, edge-weighted graphs. To address these challenges, we present Bonsai, a novel graph condensation method empowered by the observation that \textit{computation trees} form the fundamental processing units of message-passing GNNs. Bonsai condenses datasets by encoding a careful selection of \textit{exemplar} trees that maximize the representation of all computation trees in the training set. This unique approach imparts Bonsai as the first linear-time, model-agnostic graph condensation algorithm for node classification that outperforms existing baselines across $7$ real-world datasets on accuracy, while being $22$ times faster on average. Bonsai is grounded in rigorous mathematical guarantees on the adopted approximation strategies making it robust to GNN architectures, datasets, and parameters.