GraphArena: Benchmarking Large Language Models on Graph Computational Problems

The "arms race" of Large Language Models (LLMs) demands novel, challenging, and diverse benchmarks to faithfully examine their progresses. We introduce GraphArena, a benchmarking tool designed to evaluate LLMs on graph computational problems using million-scale real-world graphs from diverse scenarios such as knowledge graphs, social networks, and molecular structures. GraphArena offers a suite of 10 computational tasks, encompassing four polynomial-time (e.g., Shortest Distance) and six NP-complete challenges (e.g., Travelling Salesman Problem). It features a rigorous evaluation framework that classifies LLM outputs as correct, suboptimal (feasible but not optimal), or hallucinatory (properly formatted but infeasible). Evaluation of 10 leading LLMs, including GPT-4o and LLaMA3-70B-Instruct, reveals that even top-performing models struggle with larger, more complex graph problems and exhibit hallucination issues. Despite the application of strategies such as chain-of-thought prompting, these issues remain unresolved. GraphArena contributes a valuable supplement to the existing LLM benchmarks and is open-sourced at https://github.com/squareRoot3/GraphArena.

4DBInfer: A 4D Benchmarking Toolbox for Graph-Centric Predictive Modeling on Relational DBs

Although RDBs store vast amounts of rich, informative data spread across interconnected tables, the progress of predictive machine learning models as applied to such tasks arguably falls well behind advances in other domains such as computer vision or natural language processing. This deficit stems, at least in part, from the lack of established/public RDB benchmarks as needed for training and evaluation purposes. As a result, related model development thus far often defaults to tabular approaches trained on ubiquitous single-table benchmarks, or on the relational side, graph-based alternatives such as GNNs applied to a completely different set of graph datasets devoid of tabular characteristics. To more precisely target RDBs lying at the nexus of these two complementary regimes, we explore a broad class of baseline models predicated on: (i) converting multi-table datasets into graphs using various strategies equipped with efficient subsampling, while preserving tabular characteristics; and (ii) trainable models with well-matched inductive biases that output predictions based on these input subgraphs. Then, to address the dearth of suitable public benchmarks and reduce siloed comparisons, we assemble a diverse collection of (i) large-scale RDB datasets and (ii) coincident predictive tasks. From a delivery standpoint, we operationalize the above four dimensions (4D) of exploration within a unified, scalable open-source toolbox called 4DBInfer. We conclude by presenting evaluations using 4DBInfer, the results of which highlight the importance of considering each such dimension in the design of RDB predictive models, as well as the limitations of more naive approaches such as simply joining adjacent tables. Our source code is released at https://github.com/awslabs/multi-table-benchmark .

GraphWiz: An Instruction-Following Language Model for Graph Problems

Large language models (LLMs) have achieved impressive success across several fields, but their proficiency in understanding and resolving complex graph problems is less explored. To bridge this gap, we introduce GraphInstruct, a novel and comprehensive instruction-tuning dataset designed to equip language models with the ability to tackle a broad spectrum of graph problems using explicit reasoning paths. Utilizing GraphInstruct, we build GraphWiz, an open-source language model capable of resolving various graph problem types while generating clear reasoning processes. To enhance the model's capability and reliability, we incorporate the Direct Preference Optimization (DPO) framework into the graph problem-solving context. The enhanced model, GraphWiz-DPO, achieves an average accuracy of 65% across nine tasks with different complexity levels, surpassing GPT-4 which has an average accuracy of 43.8%. Moreover, our research delves into the delicate balance between training data volume and model performance, highlighting the potential for overfitting with increased data. We also explore the transferability of the model's reasoning ability across different graph tasks, indicating the model's adaptability and practical application potential. Our investigation offers a new blueprint and valuable insights for developing LLMs specialized in graph reasoning and problem-solving.

GADBench: Revisiting and Benchmarking Supervised Graph Anomaly Detection

With a long history of traditional Graph Anomaly Detection (GAD) algorithms and recently popular Graph Neural Networks (GNNs), it is still not clear (1) how they perform under a standard comprehensive setting, (2) whether GNNs outperform traditional algorithms such as tree ensembles, and (3) their efficiency on large-scale graphs. In response, we present GADBench -- a comprehensive benchmark for supervised anomalous node detection on static graphs. GADBench provides a thorough comparison across 23 distinct models on ten real-world GAD datasets ranging from thousands to millions of nodes ($\sim$6M). Our main finding is that tree ensembles with simple neighborhood aggregation outperform all other baselines, including the latest GNNs tailored for the GAD task. By making GADBench available as an open-source tool, we offer pivotal insights into the current advancements of GAD and establish a solid foundation for future research. Our code is available at https://github.com/squareRoot3/GADBench.

A Fused Gromov-Wasserstein Framework for Unsupervised Knowledge Graph Entity Alignment

Entity alignment is the task of identifying corresponding entities across different knowledge graphs (KGs). Although recent embedding-based entity alignment methods have shown significant advancements, they still struggle to fully utilize KG structural information. In this paper, we introduce FGWEA, an unsupervised entity alignment framework that leverages the Fused Gromov-Wasserstein (FGW) distance, allowing for a comprehensive comparison of entity semantics and KG structures within a joint optimization framework. To address the computational challenges associated with optimizing FGW, we devise a three-stage progressive optimization algorithm. It starts with a basic semantic embedding matching, proceeds to approximate cross-KG structural and relational similarity matching based on iterative updates of high-confidence entity links, and ultimately culminates in a global structural comparison between KGs. We perform extensive experiments on four entity alignment datasets covering 14 distinct KGs across five languages. Without any supervision or hyper-parameter tuning, FGWEA surpasses 21 competitive baselines, including cutting-edge supervised entity alignment methods. Our code is available at https://github.com/squareRoot3/FusedGW-Entity-Alignment.

Missing Data Imputation with Graph Laplacian Pyramid Network

Data imputation is a prevalent and important task due to the ubiquitousness of missing data. Many efforts try to first draft a completed data and second refine to derive the imputation results, or "draft-then-refine" for short. In this work, we analyze this widespread practice from the perspective of Dirichlet energy. We find that a rudimentary "draft" imputation will decrease the Dirichlet energy, thus an energy-maintenance "refine" step is in need to recover the overall energy. Since existing "refine" methods such as Graph Convolutional Network (GCN) tend to cause further energy decline, in this work, we propose a novel framework called Graph Laplacian Pyramid Network (GLPN) to preserve Dirichlet energy and improve imputation performance. GLPN consists of a U-shaped autoencoder and residual networks to capture global and local detailed information respectively. By extensive experiments on several real-world datasets, GLPN shows superior performance over state-of-the-art methods under three different missing mechanisms. Our source code is available at https://github.com/liguanlue/GLPN.

A Convergent Single-Loop Algorithm for Relaxation of Gromov-Wasserstein in Graph Data

In this work, we present the Bregman Alternating Projected Gradient (BAPG) method, a single-loop algorithm that offers an approximate solution to the Gromov-Wasserstein (GW) distance. We introduce a novel relaxation technique that balances accuracy and computational efficiency, albeit with some compromises in the feasibility of the coupling map. Our analysis is based on the observation that the GW problem satisfies the Luo-Tseng error bound condition, which relates to estimating the distance of a point to the critical point set of the GW problem based on the optimality residual. This observation allows us to provide an approximation bound for the distance between the fixed-point set of BAPG and the critical point set of GW. Moreover, under a mild technical assumption, we can show that BAPG converges to its fixed point set. The effectiveness of BAPG has been validated through comprehensive numerical experiments in graph alignment and partition tasks, where it outperforms existing methods in terms of both solution quality and wall-clock time.

Robust Attributed Graph Alignment via Joint Structure Learning and Optimal Transport

Graph alignment, which aims at identifying corresponding entities across multiple networks, has been widely applied in various domains. As the graphs to be aligned are usually constructed from different sources, the inconsistency issues of structures and features between two graphs are ubiquitous in real-world applications. Most existing methods follow the ``embed-then-cross-compare'' paradigm, which computes node embeddings in each graph and then processes node correspondences based on cross-graph embedding comparison. However, we find these methods are unstable and sub-optimal when structure or feature inconsistency appears. To this end, we propose SLOTAlign, an unsupervised graph alignment framework that jointly performs Structure Learning and Optimal Transport Alignment. We convert graph alignment to an optimal transport problem between two intra-graph matrices without the requirement of cross-graph comparison. We further incorporate multi-view structure learning to enhance graph representation power and reduce the effect of structure and feature inconsistency inherited across graphs. Moreover, an alternating scheme based algorithm has been developed to address the joint optimization problem in SLOTAlign, and the provable convergence result is also established. Finally, we conduct extensive experiments on six unsupervised graph alignment datasets and the DBP15K knowledge graph (KG) alignment benchmark dataset. The proposed SLOTAlign shows superior performance and strongest robustness over seven unsupervised graph alignment methods and five specialized KG alignment methods.

A Semi-supervised Sensing Rate Learning based CMAB Scheme to Combat COVID-19 by Trustful Data Collection in the Crowd

Mobile CrowdSensing (MCS), through employing considerable workers to sense and collect data in a participatory manner, has been recognized as a promising paradigm for building many large-scale applications in a cost-effective way, such as combating COVID-19. The recruitment of trustworthy and high-quality workers is an important research issue for MCS. Previous studies assume that the qualities of workers are known in advance, or the platform knows the qualities of workers once it receives their collected data. In reality, to reduce their costs and thus maximize revenue, many strategic workers do not perform their sensing tasks honestly and report fake data to the platform. So, it is very hard for the platform to evaluate the authenticity of the received data. In this paper, an incentive mechanism named Semi-supervision based Combinatorial Multi-Armed Bandit reverse Auction (SCMABA) is proposed to solve the recruitment problem of multiple unknown and strategic workers in MCS. First, we model the worker recruitment as a multi-armed bandit reverse auction problem, and design an UCB-based algorithm to separate the exploration and exploitation, considering the Sensing Rates (SRs) of recruited workers as the gain of the bandit. Next, a Semi-supervised Sensing Rate Learning (SSRL) approach is proposed to quickly and accurately obtain the workers' SRs, which consists of two phases, supervision and self-supervision. Last, SCMABA is designed organically combining the SRs acquisition mechanism with multi-armed bandit reverse auction, where supervised SR learning is used in the exploration, and the self-supervised one is used in the exploitation. We prove that our SCMABA achieves truthfulness and individual rationality. Additionally, we exhibit outstanding performances of the SCMABA mechanism through in-depth simulations of real-world data traces.

Handling Missing Data via Max-Entropy Regularized Graph Autoencoder

Graph neural networks (GNNs) are popular weapons for modeling relational data. Existing GNNs are not specified for attribute-incomplete graphs, making missing attribute imputation a burning issue. Until recently, many works notice that GNNs are coupled with spectral concentration, which means the spectrum obtained by GNNs concentrates on a local part in spectral domain, e.g., low-frequency due to oversmoothing issue. As a consequence, GNNs may be seriously flawed for reconstructing graph attributes as graph spectral concentration tends to cause a low imputation precision. In this work, we present a regularized graph autoencoder for graph attribute imputation, named MEGAE, which aims at mitigating spectral concentration problem by maximizing the graph spectral entropy. Notably, we first present the method for estimating graph spectral entropy without the eigen-decomposition of Laplacian matrix and provide the theoretical upper error bound. A maximum entropy regularization then acts in the latent space, which directly increases the graph spectral entropy. Extensive experiments show that MEGAE outperforms all the other state-of-the-art imputation methods on a variety of benchmark datasets.